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Speed and VelocitySpeed and Velocity
What is speed, velocity and acceleration?
How does speed, velocity and acceleration relate to Forces & Motion?
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How does MOTION relate to POSITION and TIME?How does MOTION relate to POSITION and TIME?
MOTION often includes speed and is a change in position.
QUESTION: Do you have to see something move to know that motion has taken place?
ANSWER: No – because the only thing needed is a reference point to see that something has changed position.
SPEED then is the rate of change in position or the “rate of motion.”
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Pretend you are looking at your car's speedometer while you are driving. The reading you get from
your speedometer is…
This is the speed that you are traveling at that moment.
instantaneous speed.
Measures of Speed
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Now, let’s say you are on a highway, a car may travel at the same speed for a long period of time this would be…
constant speed.
This is the speed that does not vary – cruise control.
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Now, let’s say that you are trying to determine the distance you are going to traveled in a given amount of time– this
would be…
average speed.
- - - - - - - - - - -
KatyHouston
Speed is the distance traveled per unit of time.
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Distance, Speed and Time is shown in the equation:
Calculating Speed
s =d
t
...or shortened:
s = Speed d = Distance t = Time
speed =distance
time
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Manipulating the Equation
Dmeters
Sm/s
Tseconds
multiply
divide
So, to find DISTANCE, we need to MULTIPLY speed and time.
d = s x t
The equation reads - but it can be rearranged to solve for any variable.
s =d
t
And, to find TIME, we need to DIVIDE distance by the speed.
t =d
s
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FIVE Step Approach to Solving Problems
(G )Step 1 Read the problem. Write down the GIVENS
(U) Step 2 Write down the UNKNOWNS. What you are looking
for?????
(S) Step 4 SUBSTITUTE the numbers.
(E) Step 3 Write down the EQUATION.
(S) Step 5 SOLUTION. Box Answer with UNITS!
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“A car traveled 110 miles in 2 hours.”
Consider the problem…
d =t =s =
Formula Substitute Answer
Units, units, units!
Step 1 Read the problem.Write down the GIVENS.
110 miles2 hours
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d =t =s =
Formula Substitute Answer
Units, units, units!
110 miles2 hours
“A car traveled 110 miles in 2 hours.”
110 miles2 hours
Step 2 Write down the UNKNOWNS.What are you trying to find?
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“A car traveled 110 miles in 2 hours.”
d =t =s =
Formula Substitute Answer
Units, units, units!
110 miles2 hours
Step 3 Write down the EQUATION.
s =d
t
s =d
t
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“A car traveled 110 miles in 2 hours.”
d =t =s =
Formula Substitute Answer
Units, units, units!
110 mi2 hours
Step 4 Substitute the numbers.Step 5 SOLUTION. Box Answer with Units.
55mi/hr
dt
S = 110 mi2 hr
S = 55 mi/hrS =
2 hours
110 miles
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“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
Consider the problem…
d =t =s =
Formula Substitute Answer
Units, units, units!
Step 1 Read the problem. Write down the GIVENS.
10 kmSpeed of runner:
20 km/hr
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d =
t =s =
Formula Substitute Answer
Units, units, units!
10 km
20 km/hr
Step 2 Write down the UNKNOWNS. What are you trying to find?
10 kmSpeed of runner:
20 km/hr
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
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Formula Substitute Answer
Units, units, units!
Step 3 Set up the EQUATION.
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
d =
t =s =
10 km
20 km/hrt = ds
10 km
Speed of runner: 20 km/hr
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Formula Substitute Answer
Units, units, units!
Step 4 SUBSTITUTE the numbers.Step 5 SOLUTION. Box Answer with Units.
d =
t =s =
10 km
20 km/hr
0.5 hr
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
0.5 hr
If the runner’s average speed was 20 km/hr during the 10km race, the runner’s time was 0.5 hours.
dt = s
t = 10 km
20 km/hr
19“You decide to go to Dallas to visit your friends. Your friends tell you that it takes 4 hours to get to Dallas at an average speed of 70 miles per hour. Approximately how many miles is it to their house?”Step 1 Read the problem.
Write down the GIVENS.
Step 2 Write down the UNKNOWN.
What are you trying to find?
Step 4 SUBSTITUTE the numbers.Step 5 SOLUTION. Box Answer
with units.
Step 3 Set up the EQUATION.
Formula Substitute Answer
Units, units, units!
d =
t =s =
280 mi
70 mi/hr
4 hr
?
If I drive 4 hours at 40mph, the distance from Houston to Dallas is 280 miles.
d = s x t d = 70mi/hr x 4 hr d = 280 miles
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Rate of Swimmers
0
400
800
1200
1600
2000
2400
0 5 10 15 20 25 30
Time in minutes
Dis
tanc
e in
met
ers
A distance/time graph makes it possible to “see” speed.This graph shows how fast the swimmers went during their workout.
Which swimmer swam at a constant (the same) speed throughout her workout?
Which one stopped during his/her workout?
Consta
nt spee
d
Stopped here
400 meters at 10, 15, & 20 minutes
Is a
str
aight l
ine
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What is the difference between speed and
velocity?
55 mi/hr
55 mi/h
r
55 mi/hrAll of these cars had the same SPEED but, different VELOCITIES
because they were traveling in different directions.
Velocity has speed & direction.
If you change direction, you have changed your velocity – and if you have changed your speed,
you have changed your velocity. Therefore, any change in speed OR direction is a
change in velocity!
Speed is how fast
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Acceleration … is defined as the change in velocity over time.
final velocity – initial velocity
timeacceleration =
Vf - Vi
ta =
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Types of Acceleration
• Positive Acceleration– Velocity and acceleration are in the
same direction.– Object SPEEDS up.
•Negative Acceleration–Velocity and acceleration are in opposite direction.–Object SLOWS down.
28 A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
Step 1 Read the problem. Write down the GIVENS.
top
bottom35 m/s
5 m/s
In 6 sVf =
Vi=
t =
a =
Formula Substitute Answer
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top
bottom35 m/s
5 m/s
6 sVf =
Vi=
t =
a =
Formula Substitute Answer
Step 2 Write down the UNKNOWNS.
What are you trying to find?
35 m/s
5 m/s
6 s
Finish:final
Velocity
Start:initial
Velocity
A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
30
top
bottom35 m/s
5 m/s
6 sVf =
Vi=
t =
a =
35 m/s
5 m/s
6 s
Final Velocity
InitialVelocity
Step 3 Set up the EQUATION.
Formula Substitute Answer
A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
Vf - Vi
t
Vf - Vi
t
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Vf =
Vi=
t =
a =
35 m/s
5 m/s
6 s
Formula Substitute Answer
Vf - Vi
t
35m/s – 5 m/s
6s
30 m/s
6 s= 5
m/s2
Step 4 SUBSTITUTE the numbers.Step 5 SOLUTION. Box Answer with Units.
5 m/s2
A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
The go-cart that traveled from 5m/s to 35 m/s in 6 seconds had an acceleration of 5m/s2.