1 PHYSICSMR BALDWIN Speed & Velocity9/15/2014 AIM: What is motion and how does it change? DO NOW: What do you understand about the terms speed and acceleration?

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PHYSICS MR BALDWINSpeed & Velocity

9/15/2014AIM: What is motion and how does it change?

DO NOW: What do you understand about the terms speed and acceleration?

Home Work:

Laws of Motion• Everything in the universe is in nonstop

motion.• Motion is the rule, not the exception.• The laws which govern the motion of atoms

and stars apply to the motion in our everyday lives.

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Distance and DisplacementDistinction between distance and displacement.

Distance traveled (dashed line) is a measure of length along the actual path.

Displacement (blue line) is how far the object is from its starting point, regardless of how it got there.

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Speed & VelocitySpeed: time rate of change of distance :

how far an object travels in a given time interval

Velocity includes directional information: time rate of change of displacement

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Average Speed & Instantaneous Speed• The instantaneous speed is the speed as given on your speedometer. The speed at that instant.

•Speed given by the speedometer

dv

t

• The average speed is the total distance traveled by an object divided by the total time taken to travel that distance.

CHECK: Determine the units

Unit: m/s; km/h; mph

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CHECKCHECK: : Can you write other forms Can you write other forms of the equation to determine the other of the equation to determine the other

two quantities two quantities tt & & dd??

dt =

d

=t

d v t

Problem Solving Technique: G.U.S.S.

• Givens; Unknown; Substitute & Solve

1.Write out your Givens.

2.Identify your Unknown.Check for unit consistency. If not…convert!

3.Substitute into equation (with units)Find an equation relating quantities.

4.Solve for unknown.

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QUIZ CHECK.What is the average speed of a car (in km/h & m/s) that travels 240 miles in 6 hours. Given

that 1-mile = 1.609 km = 1609 m

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PHYSICS MR BALDWINSpeed & Velocity

9/17/2014AIM: What is the difference between constant and changing motion?(What is acceleration?)DO NOW: Look at the runner below. What can you infer about the runner?

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Look at the picture below. What can you infer about the runner in red shorts?

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CHECKCHECK: : Can you write other forms Can you write other forms of the equation to determine the other of the equation to determine the other

two quantities two quantities tt & & dd??

dt =

d

=t

d v t

QUANTITY & SYMBOL

•Distance d

•Time t

•Velocity; speed v

•Mass m

UNITS

•meters (m; km; mi)

•seconds (s)

•meters/sec (m/s)– Km/h– mph

•kilogram (kg)

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• Uniform motion refers to motion that has a constant velocity– Speed & direction remains the same– Such as your car on cruise control– Moving at 50 mph on a straight road

• Accelerated motion refers to motion with changing velocity– As you round a curb– Hit the gas or brake

Uniform & Accelerated Motion

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AccelerationAcceleration is the change of velocity divided by time.

f iv va

t

Unit: m/s2Determine its Unit.

Where a: acceleration; vf: final velocity; vi:initial velocity

What is the acceleration of a car whose speed increases from 15 m/s (about 34 mi/h) to 25 m/s

(about 56 mi/h) in 20s?

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PHYSICS MR BALDWINSpeed & Velocity

9/18/2014AIM: What is motion and how does it change?

DO NOW: A skater increases his speed from 2.0 m/s to 10.0 m/s in 3.0 s. What is his acceleration?

Home Work: Worksheet 2.2

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Check

Which of the following statements correctly define acceleration?

A. Acceleration is the rate of change of displacement of an object.

B. Acceleration is the rate of change of velocity of an object.

C. Acceleration is the amount of distance covered in unit time.

D. Acceleration is the rate of change of speed of an object.

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Accelerated Motion

Acceleration is also a vector. Therefore, we need the sign.

Deceleration occurs when the acceleration is opposite in direction to the velocity.

Determine the car’s acceleration.

What can you infer about the value of the acceleration?

Check

What happens when the velocity vector and the acceleration vector of an object in motion are in same direction?

A. The acceleration of the object increases.

B. The speed of the object increases.

C. The object comes to rest.

D. The speed of the object decreases.

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A car is moving with an initial velocity of vi m/s. After reaching a highway, it moves with a constant acceleration of a m/s2, what will be the velocity (vf) of the car after traveling for t seconds?

A. vf = vi + at

B. vf = vi + 2at

C. vf2 = vi

2 + 2at

D. vf = vi – at

Check

A. vf = vi + at

B. vf = vi + 2at

C. vf2 = vi

2 + 2at

D. vf = vi – at

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PHYSICS MR BALDWINAccelerated Motion 9/19/2014

AIM: How are acceleration, velocity, distance and time related?DO NOW: Look at the runner in the red shorts below. What can you infer about the runner’s velocity and distance for each time interval?

Acceleration

There are two major indicators of the change in velocity in this motion diagram. Can you identify them?

Changing Velocity

The change in the spacing of the dots and the differences in the lengths of the velocity vectors indicate the changes in velocity.

AccelerationCan you identify which one is speeding up and which one is slowing down?

Changing Velocity

If an object speeds up, each subsequent velocity vector is longer. Also, the subsequent distances increases.

If the object slows down, … (you fill in the rest)

Acceleration

Velocity-Time Graphs

What can be said about the distances here?

Acceleration

Velocity-Time Graphs

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MATHEMATICAL

ANALYSIS OF MOTION

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The acceleration, assumed constant, is the rate of change of velocity.

Relating Acceleration, Speed & Time

f if i

v va v v at

t

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Relating Acceleration, Speed & Time

0

The acceleration is given by

We know that the average velocity is give by: 2

Substituting into the equation, we get

1

2 21

Thus,2

f i

i f

i ii

i

v va

tv v

v

v v at

v v atv v at

v v at

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Average Speed & Distance Traveled During Constant Acceleration

In addition, as the velocity is increasing at a constant rate, we know that

2

2

1Substituting into the distance equation,

21 1

we get2 2

1Thus

2

i

i i

i

v v at

d vt v at t v t at

d v t at

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Equations of Motion (Please write on Index cards)

2

2 2 2 2

For Uniform (Constant) Motion, we use

; OR

For Accelerated Motion, we use

OR

1

2

2 OR 2

f if i

i

f i f i

d dv t d v t

t v

v vv v at a

t

d v t at

v v ad v v ad

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• OBJECT STARTS FROM REST

• OBJECT RELEASED FROM REST

• OBJECT DROPPED

• OBJECT STOPS

• OBJECT COMES TO REST

• OBJECT SLOWS TO A HALT

SOME KEY PHRASES

INITIAL VELOCITY IS ZERO

FINAL VELOCITY IS ZERO

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MOTION

OF

FALLING

BODIES

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PHYSICS MR BALDWINFreefall

9/22/2014AIM: How do we describe the motion of an object in freefall?

DO NOW: In your own words, how would you define or describe freefall?

Home Work: Freefall worksheet

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Freefall Motion

Near the surface of the Earth, all objects experience approximately the same acceleration due to gravity.

Look at the image to

the left. What can you

infer about the apple’s

motion?

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Uniformly Accelerated Motion

Galileo’s Law of Freely Falling Bodies:

In the absence of air resistance, all objects, regardless of size, shape or mass, fall with the same acceleration.

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Uniformly Accelerated Motion

The acceleration due to gravity

at the Earth’s surface is

approximately 9.80 m/s2.

CHECK

• What is freefall?

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Equations of Motion

2

2 2 2 2

For Uniform (Constant) Motion, we use

; OR

For Accelerated Motion, we use

OR

1

2

2 OR 2

f if i

i

f i f i

d dv t d v t

t v

v vv v at a

t

d v t at

v v ad v v ad

Rearrange the formulas letting a = – g

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NOTE

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• The equations can be used to find time of flight from speed or distance, respectively.

• Remember that an object thrown into the air represents two mirror-image flights, one up and the other down.

• Acceleration of an object moving up is negative.• Magnitude of the acceleration up or down is the

same

PHYSICS MR BALDWIN

Freefall Motion 9/23/2014AIM: How is the motion of an object affected when projected upwards?

DO NOW: Describe the velocity of an object after it has been thrown vertically upwards with a speed of 20 m/s and returns back to it initial position.

Home Work: Worksheet - Acceleration due to gravity

Back to “HOW FAR?”• Recall that

• But for the object thrown upwards with some velocity, let d become ‘h’ (to stand for height), and vi is different from 0, with the acceleration a = -g (only due to gravity):

• DERIVE THE EQUATION FOR HEIGHT

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2id v t a t

2

2

1tgtvh i

Now to “HOW FAST?”• Recall that

• But for the object thrown upwards with some vi different from 0, with the acceleration a= -g (only due to gravity):

• DERIVE THE EQUATION FOR OBJECT’S VELOCITY.

f iv v a t

f iv v g t

From this, we can answer “HOW LONG”• If we know the height to which the object rises, we can

determine HOW LONG it takes to get there.• What happens to the velocity at the top of the object’s

motion?

• vf = 0

• DERIVE THE EQUATION FOR THE TIME TAKEN FOR THE OBJECT TO REACH MAXIMUM HEIGHT.

if i

vv v g t t

g

“HOW LONG”: What goes up must come down

• When we throw an object UP and it returns to its initial position, the total displacement is…_________

• Time of FLIGHT is duration of time object is in the air• d = 0• DERIVE THE EQUATION FOR THE TIME OF

FLIGHT

2 21 10

2 21

0 0 &2

2

i i

ii

d v t a t v t a t

v a t t tv

tg

TEST YOURSELF:A ball goes up • We have a situation to consider…The ball’s direction

of travel is in the OPPOSITE direction of its acceleration.

• THUS…• SO, what will happen to the speed as the ball rises? • DECREASE• Let’s say we gave the ball an initial upward velocity of

about 40 m/s.1. After 2 s, what will the velocity of the ball be?2. How long will the ball be in the air?3. How far will it rise in the air?

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http://phet.colorado.edu/sims/projectile-motion/projectile-motion_en.html

http://jersey.uoregon.edu/vlab/block/Block.html

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GRAPHICAL

ANALYSIS

OF

LINEAR MOTION

PHYSICS MR BALDWIN

Graphing Motion 9/29 & 30/2014

AIM: How do we graphically represent the motion of an object?

DO NOW: Draw a distance-time graph of the function

Draw a velocity-time graph of the function

You can USE your calculator.

Home Work: Worksheet - Analyzing Graphs of Motion Without Numbers

25td

tv 10

50

• Looking at the equation of motion for distance of accelerated motion, what will the resulting distance-time graph look like?

• PARABOLA

• Looking at the equation of motion for velocity of accelerated motion, what will the resulting velocity-time graph look like?

• STRAIGHT LINE (LINEAR)

CHECK

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Distance-Time graph of Uniformly Accelerated Motion

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2id v t at

0

100

200

300

400

500

600

0 5 10 15 20 25

What type of curve is this?

520

5

10

15

20

25

0 1 2 3 4 5

Finding Speed: What can you say about the slope of the graph at any time?

The slope of the tangent to the distance-time graph at any point is the instantaneous speed at that point.

4.00 m/s

8.00 m/s

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0.00

2.00

4.00

6.00

8.00

10.00

0.00 1.00 2.00 3.00 4.00 5.00

VE

LO

CIT

Y (m

/s)

TIME (s)

Speed-Time Graph of Uniformly Accelerated Motion

f iv v at What information can we gain from the Slope of the velocity-time graph?

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0.00

2.00

4.00

6.00

8.00

10.00

0.00 1.00 2.00 3.00 4.00 5.00

TIME (s)

SP

EE

D (

m/s

)Speed-Time Graph of Uniformly Accelerated Motion

f iv v at Slope gives acceleration of the body at each point.

4.00 m/s

2.00 s

Slope 2.00 m/s2

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This is a graph of d vs. t for an object moving with uniform motion.

The speed is the slope of the d-t graph.

Distance-Time graph of an object moving at Constant Speed

CHECK

Which line has the greater speed? Explain.

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Graphical Analysis of Linear MotionOn the left we have a graph of velocity-time for an object with varying velocity; on the right we have the resulting distance-time graph.

CHECKWhat can you infer about the motions of the object during periods 1 – 4?

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Graphical Analysis of Linear Motion

The distance, d, is the area beneath the velocity-time graph.

The smaller the rectangles the more precise the distance

CHECKHow would you find the area under the velocity-time graph?

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PREDICTING MOTION GRAPHS

1. Draw a distance-time graph for an object 10 m away from a starting point at rest for 10 s.

2. Draw a distance-time graph for an object moving at a constant rate of 2.0 m/s.

3. Draw a distance-time graph for an object moving at a constant rate of 4.0 m/s.

4. Draw a velocity-time graph for an object moving at a constant rate of 10 m/s.

5. Draw a velocity-time graph for an object moving at a constant rate of –10 m/s.

6. Draw a velocity-time graph for an object accelerating at a constant rate of 2.0 m/s2.

7. Draw a velocity-time graph for an object decelerating at a constant rate of 2.0 m/s2.