Claim : A statement that responds to the question asked or the problem posed. Evidence: Scientific data used to support the claim Reasoning: Using scientific.
Post on 31-Dec-2015
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bull Claim A statement that responds to the question asked or the problem posed
bull Evidence Scientific data used to support the claim
bull Reasoning Using scientific principles to show why data count as evidence to support the claim
99
1 How could you use the labquest photogates to measure the speed of your finger
2 How is it possible to be going at 200 mph and staying still at the same time
You can describe the motion of an object by its position speed direction and acceleration
Even things that appear to be at rest move When we describe the motion of one object with respect to another we say that the object is moving relative to the other object
A book that is at rest relative to the table it lies on is moving at about 30 kilometers per second relative to the sun
The book moves even faster relative to the center of our galaxy
41 Motion Is Relative
The racing cars in the Indy 500 move relative to the track
41 Motion Is Relative
When we discuss the motion of something we describe its motion relative to something else
The space shuttle moves at 8 kilometers per second relative to Earth below
A racing car in the Indy 500 reaches a speed of 300 kilometers per hour relative to the track
Unless stated otherwise the speeds of things in our environment are measured relative to the surface of Earth
41 Motion Is Relative
We will primarily use the unit meters per second (ms) for speed If a cheetah covers 50 meters in a time of 2 seconds its speed is 25 ms
42 Speed
Although you may be at rest relative to Earthrsquos surface yoursquore moving about 100000 kmh relative to the sun
41 Motion Is Relative
Before the time of Galileo people described moving things as simply ldquoslowrdquo or ldquofastrdquo Such descriptions were vague Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes Speed is how fast an object is moving
42 Speed
Motion vocab
bull Displacement ndash change in positionbull Speed ndash distance over timebull Velocity ndash displacement time
bull Or speed plus direction
Acceleration = Change in velocity time
The speedometer gives readings of instantaneous speed in both mih and kmh
42 Speed
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
99
1 How could you use the labquest photogates to measure the speed of your finger
2 How is it possible to be going at 200 mph and staying still at the same time
You can describe the motion of an object by its position speed direction and acceleration
Even things that appear to be at rest move When we describe the motion of one object with respect to another we say that the object is moving relative to the other object
A book that is at rest relative to the table it lies on is moving at about 30 kilometers per second relative to the sun
The book moves even faster relative to the center of our galaxy
41 Motion Is Relative
The racing cars in the Indy 500 move relative to the track
41 Motion Is Relative
When we discuss the motion of something we describe its motion relative to something else
The space shuttle moves at 8 kilometers per second relative to Earth below
A racing car in the Indy 500 reaches a speed of 300 kilometers per hour relative to the track
Unless stated otherwise the speeds of things in our environment are measured relative to the surface of Earth
41 Motion Is Relative
We will primarily use the unit meters per second (ms) for speed If a cheetah covers 50 meters in a time of 2 seconds its speed is 25 ms
42 Speed
Although you may be at rest relative to Earthrsquos surface yoursquore moving about 100000 kmh relative to the sun
41 Motion Is Relative
Before the time of Galileo people described moving things as simply ldquoslowrdquo or ldquofastrdquo Such descriptions were vague Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes Speed is how fast an object is moving
42 Speed
Motion vocab
bull Displacement ndash change in positionbull Speed ndash distance over timebull Velocity ndash displacement time
bull Or speed plus direction
Acceleration = Change in velocity time
The speedometer gives readings of instantaneous speed in both mih and kmh
42 Speed
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
You can describe the motion of an object by its position speed direction and acceleration
Even things that appear to be at rest move When we describe the motion of one object with respect to another we say that the object is moving relative to the other object
A book that is at rest relative to the table it lies on is moving at about 30 kilometers per second relative to the sun
The book moves even faster relative to the center of our galaxy
41 Motion Is Relative
The racing cars in the Indy 500 move relative to the track
41 Motion Is Relative
When we discuss the motion of something we describe its motion relative to something else
The space shuttle moves at 8 kilometers per second relative to Earth below
A racing car in the Indy 500 reaches a speed of 300 kilometers per hour relative to the track
Unless stated otherwise the speeds of things in our environment are measured relative to the surface of Earth
41 Motion Is Relative
We will primarily use the unit meters per second (ms) for speed If a cheetah covers 50 meters in a time of 2 seconds its speed is 25 ms
42 Speed
Although you may be at rest relative to Earthrsquos surface yoursquore moving about 100000 kmh relative to the sun
41 Motion Is Relative
Before the time of Galileo people described moving things as simply ldquoslowrdquo or ldquofastrdquo Such descriptions were vague Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes Speed is how fast an object is moving
42 Speed
Motion vocab
bull Displacement ndash change in positionbull Speed ndash distance over timebull Velocity ndash displacement time
bull Or speed plus direction
Acceleration = Change in velocity time
The speedometer gives readings of instantaneous speed in both mih and kmh
42 Speed
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
Even things that appear to be at rest move When we describe the motion of one object with respect to another we say that the object is moving relative to the other object
A book that is at rest relative to the table it lies on is moving at about 30 kilometers per second relative to the sun
The book moves even faster relative to the center of our galaxy
41 Motion Is Relative
The racing cars in the Indy 500 move relative to the track
41 Motion Is Relative
When we discuss the motion of something we describe its motion relative to something else
The space shuttle moves at 8 kilometers per second relative to Earth below
A racing car in the Indy 500 reaches a speed of 300 kilometers per hour relative to the track
Unless stated otherwise the speeds of things in our environment are measured relative to the surface of Earth
41 Motion Is Relative
We will primarily use the unit meters per second (ms) for speed If a cheetah covers 50 meters in a time of 2 seconds its speed is 25 ms
42 Speed
Although you may be at rest relative to Earthrsquos surface yoursquore moving about 100000 kmh relative to the sun
41 Motion Is Relative
Before the time of Galileo people described moving things as simply ldquoslowrdquo or ldquofastrdquo Such descriptions were vague Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes Speed is how fast an object is moving
42 Speed
Motion vocab
bull Displacement ndash change in positionbull Speed ndash distance over timebull Velocity ndash displacement time
bull Or speed plus direction
Acceleration = Change in velocity time
The speedometer gives readings of instantaneous speed in both mih and kmh
42 Speed
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
The racing cars in the Indy 500 move relative to the track
41 Motion Is Relative
When we discuss the motion of something we describe its motion relative to something else
The space shuttle moves at 8 kilometers per second relative to Earth below
A racing car in the Indy 500 reaches a speed of 300 kilometers per hour relative to the track
Unless stated otherwise the speeds of things in our environment are measured relative to the surface of Earth
41 Motion Is Relative
We will primarily use the unit meters per second (ms) for speed If a cheetah covers 50 meters in a time of 2 seconds its speed is 25 ms
42 Speed
Although you may be at rest relative to Earthrsquos surface yoursquore moving about 100000 kmh relative to the sun
41 Motion Is Relative
Before the time of Galileo people described moving things as simply ldquoslowrdquo or ldquofastrdquo Such descriptions were vague Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes Speed is how fast an object is moving
42 Speed
Motion vocab
bull Displacement ndash change in positionbull Speed ndash distance over timebull Velocity ndash displacement time
bull Or speed plus direction
Acceleration = Change in velocity time
The speedometer gives readings of instantaneous speed in both mih and kmh
42 Speed
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
When we discuss the motion of something we describe its motion relative to something else
The space shuttle moves at 8 kilometers per second relative to Earth below
A racing car in the Indy 500 reaches a speed of 300 kilometers per hour relative to the track
Unless stated otherwise the speeds of things in our environment are measured relative to the surface of Earth
41 Motion Is Relative
We will primarily use the unit meters per second (ms) for speed If a cheetah covers 50 meters in a time of 2 seconds its speed is 25 ms
42 Speed
Although you may be at rest relative to Earthrsquos surface yoursquore moving about 100000 kmh relative to the sun
41 Motion Is Relative
Before the time of Galileo people described moving things as simply ldquoslowrdquo or ldquofastrdquo Such descriptions were vague Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes Speed is how fast an object is moving
42 Speed
Motion vocab
bull Displacement ndash change in positionbull Speed ndash distance over timebull Velocity ndash displacement time
bull Or speed plus direction
Acceleration = Change in velocity time
The speedometer gives readings of instantaneous speed in both mih and kmh
42 Speed
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
We will primarily use the unit meters per second (ms) for speed If a cheetah covers 50 meters in a time of 2 seconds its speed is 25 ms
42 Speed
Although you may be at rest relative to Earthrsquos surface yoursquore moving about 100000 kmh relative to the sun
41 Motion Is Relative
Before the time of Galileo people described moving things as simply ldquoslowrdquo or ldquofastrdquo Such descriptions were vague Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes Speed is how fast an object is moving
42 Speed
Motion vocab
bull Displacement ndash change in positionbull Speed ndash distance over timebull Velocity ndash displacement time
bull Or speed plus direction
Acceleration = Change in velocity time
The speedometer gives readings of instantaneous speed in both mih and kmh
42 Speed
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
Although you may be at rest relative to Earthrsquos surface yoursquore moving about 100000 kmh relative to the sun
41 Motion Is Relative
Before the time of Galileo people described moving things as simply ldquoslowrdquo or ldquofastrdquo Such descriptions were vague Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes Speed is how fast an object is moving
42 Speed
Motion vocab
bull Displacement ndash change in positionbull Speed ndash distance over timebull Velocity ndash displacement time
bull Or speed plus direction
Acceleration = Change in velocity time
The speedometer gives readings of instantaneous speed in both mih and kmh
42 Speed
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
Before the time of Galileo people described moving things as simply ldquoslowrdquo or ldquofastrdquo Such descriptions were vague Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes Speed is how fast an object is moving
42 Speed
Motion vocab
bull Displacement ndash change in positionbull Speed ndash distance over timebull Velocity ndash displacement time
bull Or speed plus direction
Acceleration = Change in velocity time
The speedometer gives readings of instantaneous speed in both mih and kmh
42 Speed
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
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Math Reading Sci SS L Arts
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Math Reading Sci SS L Arts
Motion vocab
bull Displacement ndash change in positionbull Speed ndash distance over timebull Velocity ndash displacement time
bull Or speed plus direction
Acceleration = Change in velocity time
The speedometer gives readings of instantaneous speed in both mih and kmh
42 Speed
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
The speedometer gives readings of instantaneous speed in both mih and kmh
42 Speed
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
Average SpeedIn a trip by car the car will certainly not travel at the same speed all during the trip The driver cares about the average speed for the trip as a whole The average speed is the total distance covered divided by the time
42 Speed
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
Steps to problem solving
bull 1 What is the problem askingbull 2 What are your givensbull 3 Which equation are you going to usebull 4 plug in numbers to the equation and solve
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
910
bull See displacement velocity and acceleration google presentation
bull Whiteboarding graphs
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
911bull Construct three graphs (position vs time velocity
vs time acceleration versus time) of a person walking down the hall at a constant rate
bull What does the slope of a position time graph tell you
bull What does the slope of a velocity time graph tell you Agenda
- Turn in speed problems- Speed lab
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
914
bull Marsell the shell went 2 cm in 2 seconds stopped for another 4 seconds then moved 4 cm in 2 seconds
bull 1 How many total seconds should be in the x-axis
bull 2 Construct a position vs time graph a velocity versus time graph
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
bull What is the instantaneous velocity at 3 seconds
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
bull The positions of runner 1 and runner 2 are shown above at each second
bull bull During what time interval do the runners have the same average
velocitybull A Between 0 and 2 secondsbull B Between 0 and 3 secondsbull C Between 0 and 4 seconds
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
x x x
t t t t
curve down
x curveup
flat line
constant
v v v
tt t t
flat linev flat line
constant above zero
0
a a a
tt t t
constant below zero
aconstant above
zero constantequal to zero
0
0
Speed up(+) acceleration
Slow Down(-) acceleration
Constant Speed(0) acceleration
-moving away (+x)
Not movingNo velocity
No acceleration
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
bull Dependent variable ndash the thing that changes as a result
bull Independent variable ndash one thing that influences another
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
How to set up your graph
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
How to set up your graph
Y Axis
(This is for your dependent variable)
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
How to set up your graph
X Axis
(This is for your independent variable)
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
100
Math Reading Sci SS L Arts
01020304050
60708090
100
Math Reading Sci SS L Arts
Letrsquos Learn About Graphs
There are many different types of graphs
Letrsquos learn about two kinds
1 The bar graph
2 The line graph
0102030405060708090
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Math Reading Sci SS L Arts
01020304050
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Math Reading Sci SS L Arts
How to determine scale
bull Scale is determined by your highest amp lowest number
bull In this case your scale would be from 2 ndash 22
Favorite food
Number of Teachers
Mexican 22
Spaghetti 15
cheeseburger
11
Sushi 5
Donrsquot eat 2
How to determine Intervals
bull The interval is decided by your scale
bull In this case your scale would be from 2 ndash 22 and you want the scale to fit the graph
bull The best interval would be to go by 5rsquos
Favorite food
Number of Teachers
Mexican 22
Spaghetti 15
cheeseburger
11
Sushi 5
Donrsquot eat 2
TAILS
T - Title
Teachers favorite food
TAILS
T - Title
A - Axis
Teachersrsquos Favorite food
Y Axis = Dependent Variable
X Axis = Independent Variable
TAILS
T ndash Title
A ndash Axis
I ndash Interval
S ndash Scale
Teachersrsquos Favorite food
The amount of space between one number and the next or one type of data and the next on the graph
The interval is just as important as the scale
Choose an interval that lets you make the graph as large as possible for your paper and data
TAILS
T ndash Title
A ndash Axis
I ndash Interval
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
TAILS
T ndash Title
A ndash Axis
I ndash Interval
L ndash Labels
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
Mexican
Spaghetti
Cheeseburger
Sushi
Donrsquot eat
LABEL your bars or data points
Singers
Give the bars a general label What do those words mean
Num
ber
of T
each
ers
Label your Y Axis What do those numbers mean
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 2 holes
Position (cm)
Spee
d (c
ms
)
916
915 Complete the table in your notebook
Agenda- Velocity discussion- Acceleration discussion- Acceleration practice
Animal Distance Time Speed
Cheetah 75 m 3 s 25 ms
Greyhound 160 m 10 s
Gazelle 1 km 100 km h
Turtle 30 s 1 cm s
42 Speed
We can change the state of motion of an object by changing its speed its direction of motion or both Acceleration is the rate at which the velocity is changing
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
How to determine Intervals
bull The interval is decided by your scale
bull In this case your scale would be from 2 ndash 22 and you want the scale to fit the graph
bull The best interval would be to go by 5rsquos
Favorite food
Number of Teachers
Mexican 22
Spaghetti 15
cheeseburger
11
Sushi 5
Donrsquot eat 2
TAILS
T - Title
Teachers favorite food
TAILS
T - Title
A - Axis
Teachersrsquos Favorite food
Y Axis = Dependent Variable
X Axis = Independent Variable
TAILS
T ndash Title
A ndash Axis
I ndash Interval
S ndash Scale
Teachersrsquos Favorite food
The amount of space between one number and the next or one type of data and the next on the graph
The interval is just as important as the scale
Choose an interval that lets you make the graph as large as possible for your paper and data
TAILS
T ndash Title
A ndash Axis
I ndash Interval
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
TAILS
T ndash Title
A ndash Axis
I ndash Interval
L ndash Labels
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
Mexican
Spaghetti
Cheeseburger
Sushi
Donrsquot eat
LABEL your bars or data points
Singers
Give the bars a general label What do those words mean
Num
ber
of T
each
ers
Label your Y Axis What do those numbers mean
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 2 holes
Position (cm)
Spee
d (c
ms
)
916
915 Complete the table in your notebook
Agenda- Velocity discussion- Acceleration discussion- Acceleration practice
Animal Distance Time Speed
Cheetah 75 m 3 s 25 ms
Greyhound 160 m 10 s
Gazelle 1 km 100 km h
Turtle 30 s 1 cm s
42 Speed
We can change the state of motion of an object by changing its speed its direction of motion or both Acceleration is the rate at which the velocity is changing
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
TAILS
T - Title
Teachers favorite food
TAILS
T - Title
A - Axis
Teachersrsquos Favorite food
Y Axis = Dependent Variable
X Axis = Independent Variable
TAILS
T ndash Title
A ndash Axis
I ndash Interval
S ndash Scale
Teachersrsquos Favorite food
The amount of space between one number and the next or one type of data and the next on the graph
The interval is just as important as the scale
Choose an interval that lets you make the graph as large as possible for your paper and data
TAILS
T ndash Title
A ndash Axis
I ndash Interval
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
TAILS
T ndash Title
A ndash Axis
I ndash Interval
L ndash Labels
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
Mexican
Spaghetti
Cheeseburger
Sushi
Donrsquot eat
LABEL your bars or data points
Singers
Give the bars a general label What do those words mean
Num
ber
of T
each
ers
Label your Y Axis What do those numbers mean
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 2 holes
Position (cm)
Spee
d (c
ms
)
916
915 Complete the table in your notebook
Agenda- Velocity discussion- Acceleration discussion- Acceleration practice
Animal Distance Time Speed
Cheetah 75 m 3 s 25 ms
Greyhound 160 m 10 s
Gazelle 1 km 100 km h
Turtle 30 s 1 cm s
42 Speed
We can change the state of motion of an object by changing its speed its direction of motion or both Acceleration is the rate at which the velocity is changing
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
TAILS
T - Title
A - Axis
Teachersrsquos Favorite food
Y Axis = Dependent Variable
X Axis = Independent Variable
TAILS
T ndash Title
A ndash Axis
I ndash Interval
S ndash Scale
Teachersrsquos Favorite food
The amount of space between one number and the next or one type of data and the next on the graph
The interval is just as important as the scale
Choose an interval that lets you make the graph as large as possible for your paper and data
TAILS
T ndash Title
A ndash Axis
I ndash Interval
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
TAILS
T ndash Title
A ndash Axis
I ndash Interval
L ndash Labels
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
Mexican
Spaghetti
Cheeseburger
Sushi
Donrsquot eat
LABEL your bars or data points
Singers
Give the bars a general label What do those words mean
Num
ber
of T
each
ers
Label your Y Axis What do those numbers mean
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 2 holes
Position (cm)
Spee
d (c
ms
)
916
915 Complete the table in your notebook
Agenda- Velocity discussion- Acceleration discussion- Acceleration practice
Animal Distance Time Speed
Cheetah 75 m 3 s 25 ms
Greyhound 160 m 10 s
Gazelle 1 km 100 km h
Turtle 30 s 1 cm s
42 Speed
We can change the state of motion of an object by changing its speed its direction of motion or both Acceleration is the rate at which the velocity is changing
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
TAILS
T ndash Title
A ndash Axis
I ndash Interval
S ndash Scale
Teachersrsquos Favorite food
The amount of space between one number and the next or one type of data and the next on the graph
The interval is just as important as the scale
Choose an interval that lets you make the graph as large as possible for your paper and data
TAILS
T ndash Title
A ndash Axis
I ndash Interval
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
TAILS
T ndash Title
A ndash Axis
I ndash Interval
L ndash Labels
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
Mexican
Spaghetti
Cheeseburger
Sushi
Donrsquot eat
LABEL your bars or data points
Singers
Give the bars a general label What do those words mean
Num
ber
of T
each
ers
Label your Y Axis What do those numbers mean
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 2 holes
Position (cm)
Spee
d (c
ms
)
916
915 Complete the table in your notebook
Agenda- Velocity discussion- Acceleration discussion- Acceleration practice
Animal Distance Time Speed
Cheetah 75 m 3 s 25 ms
Greyhound 160 m 10 s
Gazelle 1 km 100 km h
Turtle 30 s 1 cm s
42 Speed
We can change the state of motion of an object by changing its speed its direction of motion or both Acceleration is the rate at which the velocity is changing
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
TAILS
T ndash Title
A ndash Axis
I ndash Interval
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
TAILS
T ndash Title
A ndash Axis
I ndash Interval
L ndash Labels
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
Mexican
Spaghetti
Cheeseburger
Sushi
Donrsquot eat
LABEL your bars or data points
Singers
Give the bars a general label What do those words mean
Num
ber
of T
each
ers
Label your Y Axis What do those numbers mean
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 2 holes
Position (cm)
Spee
d (c
ms
)
916
915 Complete the table in your notebook
Agenda- Velocity discussion- Acceleration discussion- Acceleration practice
Animal Distance Time Speed
Cheetah 75 m 3 s 25 ms
Greyhound 160 m 10 s
Gazelle 1 km 100 km h
Turtle 30 s 1 cm s
42 Speed
We can change the state of motion of an object by changing its speed its direction of motion or both Acceleration is the rate at which the velocity is changing
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
TAILS
T ndash Title
A ndash Axis
I ndash Interval
L ndash Labels
S ndash Scale
Teachersrsquos Favorite food
0
5
10
15
20
25
Mexican
Spaghetti
Cheeseburger
Sushi
Donrsquot eat
LABEL your bars or data points
Singers
Give the bars a general label What do those words mean
Num
ber
of T
each
ers
Label your Y Axis What do those numbers mean
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 2 holes
Position (cm)
Spee
d (c
ms
)
916
915 Complete the table in your notebook
Agenda- Velocity discussion- Acceleration discussion- Acceleration practice
Animal Distance Time Speed
Cheetah 75 m 3 s 25 ms
Greyhound 160 m 10 s
Gazelle 1 km 100 km h
Turtle 30 s 1 cm s
42 Speed
We can change the state of motion of an object by changing its speed its direction of motion or both Acceleration is the rate at which the velocity is changing
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 2 holes
Position (cm)
Spee
d (c
ms
)
916
915 Complete the table in your notebook
Agenda- Velocity discussion- Acceleration discussion- Acceleration practice
Animal Distance Time Speed
Cheetah 75 m 3 s 25 ms
Greyhound 160 m 10 s
Gazelle 1 km 100 km h
Turtle 30 s 1 cm s
42 Speed
We can change the state of motion of an object by changing its speed its direction of motion or both Acceleration is the rate at which the velocity is changing
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
915 Complete the table in your notebook
Agenda- Velocity discussion- Acceleration discussion- Acceleration practice
Animal Distance Time Speed
Cheetah 75 m 3 s 25 ms
Greyhound 160 m 10 s
Gazelle 1 km 100 km h
Turtle 30 s 1 cm s
42 Speed
We can change the state of motion of an object by changing its speed its direction of motion or both Acceleration is the rate at which the velocity is changing
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
42 Speed
We can change the state of motion of an object by changing its speed its direction of motion or both Acceleration is the rate at which the velocity is changing
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
We can change the state of motion of an object by changing its speed its direction of motion or both Acceleration is the rate at which the velocity is changing
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Speed and velocity are measured in units of distance per timeAcceleration is the change in velocity (or speed) per time
intervalAcceleration units are speed per time Changing speed without changing direction from 0 kmh to 10
kmh in 1 second acceleration along a straight line is
44 Acceleration
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
A car is accelerating whenever there is a change in its state of motion
44 Acceleration
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Accelerate in the direction of velocityndashspeed upAccelerate against velocityndashslow downAccelerate at an angle to velocityndashchange direction
44 Acceleration
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
In other words the car speeds up from 35 kmh to 50 kmh in 3 seconds What is the acceleration
44 Acceleration
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
41 Acceleration
bull Acceleration is the rate of change in the speed of an object
bull Rate of change means the ratio of the amount of change divided by how much time the change takes
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
41 Acceleration in metric units
bull If a carrsquos speed increases from 89 ms to 27 ms the acceleration in metric units is 181 ms divided by 4 seconds or 45 meters per second per second
bull Meters per second per second is usually written as meters per second squared (ms2)
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
41 The difference between velocity and acceleration
bull Velocity is fundamentally different from acceleration
bull Velocity can be positive or negative and is the rate at which an objectrsquos position changes
bull Acceleration is the rate at which velocity changes
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Inv 41 Acceleration
Investigation Key QuestionHow does acceleration relate to velocity
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
41 The difference between velocity and acceleration
bull The acceleration of an object can be in the same direction as its velocity or in the opposite direction
bull Velocity increases when acceleration is in the same direction
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
41 Calculating acceleration
bull The formula for acceleration can also be written in a form that is convenient for experiments
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
41 Calculating acceleration
bull Acceleration is the change in velocity divided by the change in time The Greek letter delta (Δ) means ldquothe change inrdquo
a = Dv Dt
Change in speed (msec)
Change in time (sec)
Acceleration (msec2)
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull Predict what the speed is going to be at for 70 cm
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
speed vs position at 8 cm
Position (cm)
Spee
d (c
ms
)
916
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Find the initial velocity through the first photogate in cms Remember the distance of the flag is one cm initial velocity 1 cm01373 s = 7283 cm s
Find the final velocity through the second photogateFinal velocity is 1 (36240-35680)= 17857
How could use photogates to measure time on the trackFinal time ndash initial time = 35680 - 0000 = 35680 s
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull How could you find accelerationbull Vf ndash Vi T
Change in velocity (17857 cms ndash 7283 cm s ) = 10574 cms
Acceleration 10574 3568 = 29635 cmss
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
1 You are asked for acceleration2 You are given times and speeds from an
experiment3 Use the relationship a = (v2 ndash v1) divide (t2 ndash t1)4 Choose any two pairs of time and speed data
since the change in speed is constantndash a = (6 ms 4 ms) divide (3 s ndash 4 s) = (2 ms) divide (-1 s)ndash a = minus2 ms
Calculating acceleration in ms2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill A partner records the speed of the bicycle every second for five seconds Calculate the acceleration of the bicycle
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
41 Constant negative acceleration
bull Consider a ball rolling up a ramp
bull As the ball slows down eventually its speed becomes zero and at that moment the ball is at rest
bull However the ball is still accelerating because its velocity continues to change
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull httpwwwglencoecomsecscienceinternet_labimagesphysicsCh1mov
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Fill out the following table
bull Challenge try to find a formula for time
Time Acceleration
V final V average Distance traveled
0 10 mss 0 ms 0 ms 0 m
1 10 mss 10 ms 5 ms 5 m
2 10 mss
3 10 mss
4 10 mss
5 10 mss
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
94
bull 1 What is the difference between speed and velocity
bull 2 If you are traveling at 60 mph how long would it take you to travel 180 miles Show your work
bull Agenda Aces high
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
98
bull What were the main differences between a fast flier and a slow flier
bull What are some modifications you made
Due today
Lab report on paper planesThe summary should include discussion on how your followed the enginnering and design process
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull What sort of data could you takebull Timebull Distance speedbull Dimensions of your planebull How do you measure speed
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Concept check
1 You are running at 5 ms towards a wall that is 10 meters away how long before you hit it
2 You are running at the same wall at 2 ms and you hit it 5 seconds later how far away is the wall
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull httpphetcoloradoeduensimulationmoving-man
bull What is the relationship between time and velocity
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
thinkSuppose a car moving in a straight line steadily increases its speed each second first from 35 to 40 kmh then from 40 to 45 kmh then from 45 to 50 kmh What is its acceleration
Answer The speed increases by 5 kmh during each 1-s interval in a straight line The acceleration is therefore 5 kmhbulls during each interval
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
44 Acceleration
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
thinkIn 5 seconds a car moving in a straight line increases its speed from 50 kmh to 65 kmh while a truck goes from rest to 15 kmh in a straight line Which undergoes greater acceleration What is the acceleration of each vehicle
Answer The car and truck both increase their speed by 15 kmh during the same time interval so their acceleration is the same
44 Acceleration
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Falling ObjectsImagine there is no air resistance and that gravity is the only thing affecting a falling object
An object moving under the influence of the gravitational force only is said to be in free fall
The elapsed time is the time that has elapsed or passed since the beginning of any motion in this case the fall
45 Free Fall How Fast
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull On Jupiter A ball starts at 5 ms and travels down a ramp and gains a speed of 35 ms in 3 seconds What is the balls acceleration
bull Light travels in a straight line at a constant speed of 300000 kms what is the lights acceleration
bull Create a bubble map around the word flight
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
What is engineering
bull httpwwwdiscoverengineeringorg
bull Types of engineeringbull Nuclearbull Medicalbull Mechanicalbull Chemicalbull Electrical
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Engineering and design process
bull 1 Identify the problembull 2 Identify criteria and constraintsbull 3 Brainstorm possible solutionsbull 4 Generate ideasbull 5 Explore possibilitiesbull 6 Select an approachbull 7 build a modelbull Refine the design
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull What do you need in order to finish your lab report
httpscience360govobjtkn-videofc729ef0-22ee-4f61-bb2a-b6c07685fb02science-nfl-football-projectile-motion-parabolas
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Perigrine falcon dive
httpwwwyoutubecomwatchv=legzXQlFNjs
httpwwwyoutubecomwatchv=IyFofv8ZqdEampfeature=related
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Early flight
httpwwwyoutubecomwatchv=iMhdksPFhCM
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
218
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each
runner graphically after each second (see handout)
bull 2 Try again with a runner that is traveling at a constant 3 ms
Turn in plane lab
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
The Cheetah A cat that is built for speed Its strength and agility allow it to sustain a top speed of over 100 kmh Such speeds can only be maintained for about ten seconds
Photo copy Vol 44 Photo DiskGetty
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Objectives After completing this module you should be able to
bull Define and apply concepts of average and instantaneous velocity and acceleration
bull Solve problems involving initial and final velocity acceleration displacement and time
bull Demonstrate your understanding of directions and signs for velocity displacement and acceleration
bull Solve problems involving a free-falling body in a gravitational field
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Uniform Acceleration in One Dimension
bull Motion is along a straight line (horizontal vertical or slanted)
bull Changes in motion result from a CONSTANT force producing uniform acceleration
bull The cause of motion will be discussed later Here we only treat the changes
bull The moving object is treated as though it were a point particle
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Distance and DisplacementDistance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
Distance is the length of the actual path taken by an object Consider travel from point A to point B in diagram below
A
Bs = 20 m
Distance s is a scalar quantity (no direction)
Contains magnitude only and consists of a number and a unit
(20 m 40 mih 10 gal)
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Distance and DisplacementDisplacement is the straight-line separation of two points in a specified directionDisplacement is the straight-line separation of two points in a specified direction
A vector quantityContains magnitude AND direction a number unit amp angle(12 m 300 8 kmh N)
A
BD = 12 m 20o
q
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Distance and Displacementbull For motion along x or y axis the displacement is
determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
bull For motion along x or y axis the displacement is determined by the x or y coordinate of its final position Example Consider a car that travels 8 m E then 12 m W
Net displacement D is from the origin to the final position
What is the distance traveled 20 m
12 mW
D
D = 4 m WD = 4 m W
x8 mE
x = +8x = -4
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
The Signs of Displacementbull Displacement is positive (+) or negative
(-) based on LOCATION
2 m
-1 m
-2 m
The displacement is the y-coordinate Whether motion is up or down + or - is based on LOCATION
Examples
The direction of motion does not matterThe direction of motion does not matter
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Definition of Speed
bull Speed is the distance traveled per unit of time (a scalar quantity)
bull Speed is the distance traveled per unit of time (a scalar quantity)
v = = st
20 m 4 s
v = 5 msv = 5 ms
Not direction dependent
A
Bs = 20 m
Time t = 4 s
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Definition of Velocity
bull Velocity is the displacement per unit of time (A vector quantity)
bull Velocity is the displacement per unit of time (A vector quantity)
v = 3 ms at 200 N of Ev = 3 ms at 200 N of E
Direction required
A
Bs = 20 m
Time t = 4 s
12 m
4 s
Dv
t
D=12 m
20o
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Example 1 A runner runs 200 m east then changes direction and runs 300 m west If the entire trip takes 60 s what is the
average speed and what is the average velocity
Recall that average speed is a function only of total distance and total time
Total distance s = 200 m + 300 m = 500 m
500 m
60 s
total pathAverage speed
time
Avg speed 833 ms
Direction does not matter
start
s1 = 200 ms2 = 300 m
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Example 1 (Cont) Now we find the average velocity which is the net displacement divided by time In this case the
direction matters
xo = 0
t = 60 s
x1= +200 mxf = -100 m0fx xv
t
x0 = 0 m xf = -100 m
Direction of final displacement is to the left as shown
Average velocity 167 ms Westv
Note Average velocity is directed to the west
100 m 0167 ms
60 sv
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Example 2 A sky diver jumps and falls for 600 m in 14 s After chute opens he falls another 400 m in 150 s What
is average speed for entire fall
625 m
356 m
14 s
142 s
A
B
600 m + 400 m
14 s + 150 sA B
A B
x xv
t t
1000 m
164 sv 610 msv
Average speed is a function only of total distance traveled and the total time required
Average speed is a function only of total distance traveled and the total time required
Total distance total time
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Examples of Speed
Light = 3 x 108 ms
Orbit 2 x 104 ms
Jets = 300 ms Car = 25 ms
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Speed Examples (Cont)
Runner = 10 ms
Snail = 0001 ms
Glacier = 1 x 10-5 ms
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Average Speed and Instantaneous Velocity
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant (v at point C)
The average speed depends ONLY on the distance traveled and the time required
The average speed depends ONLY on the distance traveled and the time required
A
Bs = 20 m
Time t = 4 s
C
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
The Signs of Velocity
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
First choose + direction then v is positive if motion is with that direction and negative if it is against that direction
Velocity is positive (+) or negative (-) based on direction of motion
Velocity is positive (+) or negative (-) based on direction of motion
-+
-++
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
219
bull Is a track athlete more likely to report their velocity or speed Is it more likely to be an average or instantaneous
bull The speed of sound is about 340 meters per second If you shout h-el-l-o and hear your voice 24 seconds later how far are you from the cliff wall
bull Agenda Warm upbull moving man exercisebull finish practice problems
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull httpphetcoloradoeduensimulationmoving-manbull Record three patterns you noticed in the graphs
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
220
bull 1 Draw a quick representation of a particle going in constant motion and one going in accelerated motion (number line or xy cartesian graph)
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
223
1 What is one thing you are going to investigate
2 You walk up to the wall slowly for 3 seconds stop for 2 seconds then back up quickly for one second to your original spot Create the following graphs of this situation a Position vs timeb Velocity vs timec Acceleration vs time
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull Present at end of hourbull Create a claim evidence and reasoning sheet
and share out one thing your group has discovered
bull Claim What did you find out bull Evidence What did your graphs show Draw
pictures of your graphs
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
921
1 Who will win a 20 meter race some one who is running at a constant 2 ms or some one who is starting from 0 but has an acceleration at 1 ms bull Draw two number lines and represent each runner graphically after each second (see
handout)
Try again with a runner that is traveling at a constant 3 ms
2 Usain Bolt broke the worldrsquos record when he ran the 100 meter in under 10 seconds What was his speed in ms
bull httpswwwyoutubecomwatchv=QSYObch2nNI
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
1 Create a velocity time graph of what you think this looks like (remember to label)
2 Do the same for a distance time graph
3 An acceleration time graph 4 Now add a cheetah to your graphshttpswwwyoutubecomwatchv=Km2JDIR8-8I
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull What causes the cheetah and the sprinter to accelerate
bull What is the formula for acceleration
bull Acceleration -practice
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
bull A soccer player ran west down the field for 80 meters then back east for 40 meters It took her 20 seconds
bull What is the average velocity
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Average and Instantaneous v
Dx
Dt
x2
x1
t2t1
2 1
2 1avg
x x xv
t t t
( 0)inst
xv t
t
Dx
Dt
Time
slope
Dis
plac
emen
t x
Average Velocity Instantaneous Velocity
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Definition of Acceleration An acceleration is the change in
velocity per unit of time (A vector quantity)
A change in velocity requires the application of a push or pull (force)
A formal treatment of force and acceleration will be given later For now you should know that
bull The direction of accel- eration is same as direction of force
bull The acceleration is proportional to the magnitude of the force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force
Acceleration and Force
F
a
2F 2a
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Example of Acceleration
The wind changes the speed of a boat from 2 ms to 8 ms in 3 s Each second the speed changes by 2 ms
Wind force is constant thus acceleration is constantWind force is constant thus acceleration is constant
+
vf = +8 ms v0 = +2 ms
t = 3 s
Force
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
The Signs of Accelerationbull Acceleration is positive (+) or negative (-)
based on the direction of forcebull Acceleration is positive (+) or negative (-)
based on the direction of force
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
Choose + direction first Then acceleration a will have the same sign as that of the force F mdashregardless of the direction of velocity
F
F
+a (-)
a(+)
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Average and Instantaneous a
Dv
Dt
v2
v1
t2t1
Dv
Dt
time
slope
2 1
2 1avg
v v va
t t t
( 0)inst
va t
t
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Example 3 (No change in direction) A constant force changes the speed of a car from 8 ms to 20 ms in 4 s
What is average acceleration
Step 1 Draw a rough sketch Step 2 Choose a positive direction (right)
Step 3 Label given info with + and - signs
Step 4 Indicate direction of force F
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Example 3 (Continued) What is average acceleration of car
Step 5 Recall definition of average
acceleration
2 1
2 1avg
v v va
t t t
20 ms - 8 ms3 ms
4 sa
3 ms rightwarda
+
v1 = +8 ms
t = 4 s
v2 = +20 ms
Force
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Example 4 A wagon moving east at 20 ms encounters a very strong head-wind causing it to
change directions After 5 s it is traveling west at 5 ms What is the average acceleration (Be careful
of signs)
Step 1 Draw a rough sketch
+ Force
Step 2 Choose the eastward direction as positive
vo = +20 ms vf = -5 ms
Step 3 Label given info with + and - signs
E
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Example 4 (Cont) Wagon moving east at 20 ms encounters a head-wind causing it to change
directions Five seconds later it is traveling west at 5 ms What is the average acceleration
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Choose the eastward direction as positiveInitial velocity vo = +20 ms east (+)Final velocity vf = -5 ms west (-)The change in velocity Dv = vf - v0
Dv = (-5 ms) - (+20 ms) = -25 ms
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Example 4 (Continued)
aavg = =DvDt
vf - vo
tf - to a =
-25 ms 5 s
a = - 5 ms2 a = - 5 ms2Acceleration is directed to left west (same as F)
+ Force
vo = +20 ms vf = -5 ms
E
Dv = (-5 ms) - (+20 ms) = -25 ms
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Signs for Displacement
Time t = 0 at point A What are the signs (+ or -) of displacement at B C and DAt B x is positive right of origin
At C x is positive right of origin
At D x is negative left of origin
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
What are the signs (+ or -) of acceleration at points B C
and D
The force is constant and always directed to left so acceleration does not change
At B C and D a = -5 ms negative at all points
Signs for Acceleration
+ Force
vo = +20 ms vf = -5 ms
E a = - 5 ms2
A BCD
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
DefinitionsAverage velocity
Average acceleration
2 1
2 1avg
x x xv
t t t
2 1
2 1avg
v v va
t t t
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Velocity for constant aAverage velocity Average velocity
Setting to = 0 and combining we have
0
0
favg
f
x xxv
t t t
0
2f
avg
v vv
00 2
fv vx x t
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
225
bull Objects that are freefalling have an acceleration of 10 mss You drop a rock off a bridge 3 seconds later you here a splash
bull How fast was it going after 3 secondsbull What was the average speedbull How far did it go
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
45 Free Fall How Fast
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
thinkWhat would the speedometer reading on the falling rock be 45 seconds after it drops from rest How about 8 seconds after it is dropped
Answer The speedometer readings would be 45 ms and 80 ms respectively
45 Free Fall How Fast
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0 10 0 0 0
1 10 10 5 5
2 10 20 10 20
3 10 30 15 45
4 10 40 20 80
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
Fill in the chart
bull What is the relationship between distance traveled and time
Time (s) Acceleration (mss)
Final velocity (ms)
Average velocity (ms)
Distance (m)
0
1
2
3
4
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
These distances form a mathematical pattern at the end of time t the object starting from rest falls a distance d
46 Free Fall How Far
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
46 Free Fall How Far
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
45 Free Fall How Fast
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
226bull Is the unit of light year a speed distance or
time
bull Consider an object being dropped in a vacuum (see video)
bull A Create an acceleration versus time graphbull B a velocity versus time graph bull C a position versus time graph
Notebook check217- 226Skip 10
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
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- 226
- Slide 132
bull Brian Cox visits the worlds biggest vacuum chamber
bull httpswwwyoutubecomwatchv=E43-CfukEgs
- Slide 1
- Slide 2
- 99
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- Motion vocab
- Slide 12
- Slide 13
- Steps to problem solving
- 910
- 911
- 914
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- Slide 21
- How to set up your graph
- How to set up your graph (2)
- How to set up your graph (3)
- Letrsquos Learn About Graphs
- How to determine scale
- How to determine Intervals
- TAILS
- TAILS (2)
- TAILS (3)
- TAILS (4)
- TAILS (5)
- Slide 33
- 915 Complete the table in your notebook
- Slide 35
- Slide 36
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- Slide 39
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- Slide 41
- Slide 42
- 41 Acceleration
- 41 Acceleration in metric units
- 41 The difference between velocity and acceleration
- Inv 41 Acceleration
- 41 The difference between velocity and acceleration (2)
- 41 Calculating acceleration
- 41 Calculating acceleration (2)
- Slide 50
- Slide 51
- Slide 52
- Calculating acceleration in ms2
- 41 Constant negative acceleration
- Slide 55
- Slide 56
- Fill out the following table
- 94
- 98
- Slide 60
- Concept check
- Slide 62
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- Slide 68
- What is engineering
- Slide 70
- Slide 71
- Engineering and design process
- Slide 73
- Slide 74
- Early flight
- 218
- Slide 77
- Objectives After completing this module you should be able to
- Uniform Acceleration in One Dimension
- Distance and Displacement
- Distance and Displacement (2)
- Distance and Displacement (3)
- The Signs of Displacement
- Definition of Speed
- Definition of Velocity
- Example 1 A runner runs 200 m east then changes direction an
- Example 1 (Cont) Now we find the average velocity which is th
- Example 2 A sky diver jumps and falls for 600 m in 14 s After
- Examples of Speed
- Speed Examples (Cont)
- Average Speed and Instantaneous Velocity
- The Signs of Velocity
- 219
- Slide 94
- 220
- 223
- Slide 97
- 921
- Slide 99
- Slide 100
- Slide 101
- Average and Instantaneous v
- Definition of Acceleration
- Acceleration and Force
- Example of Acceleration
- The Signs of Acceleration
- Average and Instantaneous a
- Example 3 (No change in direction) A constant force changes th
- Example 3 (Continued) What is average acceleration of car
- Example 4 A wagon moving east at 20 ms encounters a very stro
- Example 4 (Cont) Wagon moving east at 20 ms encounters a hea
- Slide 112
- Slide 113
- Slide 114
- Definitions
- Velocity for constant a
- Slide 117
- 225
- Slide 119
- Slide 120
- Fill in the chart
- Fill in the chart (2)
- Fill in the chart (3)
- Fill in the chart (4)
- Fill in the chart (5)
- Fill in the chart (6)
- Fill in the chart (7)
- Slide 128
- Slide 129
- Slide 130
- 226
- Slide 132
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