Speed and Velocity
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Transcript of Speed and Velocity
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Speed and VelocitySpeed and Velocity
What is speed, velocity and acceleration?
Speed and VelocitySpeed and Velocity
(Use with Speed, Velocity and Acceleration handout)
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speed =distance
time
Speed is the distance traveled per unit of time.
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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…
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Average speed is the distance traveled divided by the time. It can be calculated
using the following formula:
speed =distance
time
s =d
t
...or shortened:
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Four Step Approach to Solving Problems
Step 1 Read the problem. Draw a picture.
Step 2 Write down what you know. What are you trying to find?
Step 4 Plug-in the numbers.Solve.
Step 3 Set up the formula.
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“A car traveled 110 miles in 2 hours.”
Consider the problem…
d =t =s =
Formula Plug-in Answer
Units, units, units!
Step 1 Read the problem.Draw a picture.
110 miles2 hours
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“A car traveled 110 miles in 2 hours.”
d =t =s =
Formula Plug-in Answer
Units, units, units!
110 miles2 hours
Step 2 Write down what you know.What are you trying to find?
110 miles2 hours
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“A car traveled 110 miles in 2 hours.”
d =t =s =
Formula Plug-in Answer
Units, units, units!
110 miles2 hours
Step 3 Set up the formula.
s =d
t
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“A car traveled 110 miles in 2 hours.”
d =t =s =
Formula Plug-in Answer
Units, units, units!
110 miles2 hours
Step 3 Set up the formula.
dt
S =
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“A car traveled 110 miles in 2 hours.”
d =t =s =
Formula Plug-in Answer
Units, units, units!
110 mi2 hours
Step 4 Plug-in the numbers.Solve.
dt
110 mi2 hr 55 mi/hr55mi/hr
55 mi/hr
S = S = S =
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Do the problems 1-3 on your notes.
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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 Plug-in Answer
Units, units, units!
Step 1 Read the problem. Draw a picture.
10 kmSpeed of runner:
20 km/hr
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d =
t =s =
Formula Plug-in Answer
Units, units, units!
10 km
20 km/hr
Step 2 Write down what you know. 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 Plug-in Answer
Units, units, units!
Step 3 Set up the formula.
“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/hr
s = d
t
s (km/hr) = d (km)
t (hr)
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Formula Plug-in Answer
Units, units, units!
Step 4 Plug-in the numbers.Solve.
10 km20 km
d =
t =s =
10 km
20 km/hr
.5 hr
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
Time: 0.5 Hour
S = d
tt (hr)
= 10 km20 km x t (hr)
=1 Hr (t)
Proportion Problem… Cross multiply and divide…
.5 hr
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Do the problems 4-5 on your notes.
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“You decide to go to Dallas to see 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.
Draw a picture.Step 2 Write down what you know.
What are you trying to find?
Step 4 Plug-in the numbers.Solve.
Step 3 Set up the formula.
Formula Plug-in Answer
Units, units, units!
d =
t =s =
280 mi
70 mi/hr
4 hr
?
70 miles per hour4 hours
s = d / t70 mi/hr = d/4 hr
70 mi1 hr
= d (mi)
4 hr
70mi x 4hrd x 1hr
=280 mi
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Do problem 6 on your notes.
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Instantaneous speed (Reading on your speedometer)
and average speed do not involve direction.
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What is the difference between speed and
velocity?
55 mi/hr
55 mi/h
r
55 mi/hr
All of these cars had different velocities
because they were traveling in different directions.
Velocity has speed & direction.
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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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Make the speed graph& answer the questions.
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Acceleration
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Acceleration is defined as the
change in velocity over time.
(change) in velocity
timeacceleration =
final velocity – initial velocity
timeacceleration =
Vf - Vi
ta =
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25 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. Draw a picture.
top
bottom35 m/s
5 m/s
In 6 sVf =
Vi=
t =
a =
Formula Plug-in Answer
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top
bottom35 m/s
5 m/s
6 sVf =
Vi=
t =
a =
Formula Plug-in Answer
Step 2 Write down what you know. What are you trying to find?
35 m/s
5 m/s
6 s
Finish:final
Velocity
Start:initial
Velocity
final velocity – initial velocitytimeacceleration =
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?
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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 formula.
Formula Plug-in
Vf - Vi
t
Answer
Vf - Vi
t
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?
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Vf =
Vi=
t =
a =
Formula Plug-in Answer35 m/s
5 m/s
6 s
Vf - Vi
t
35m/s – 5 m/s
6s
30 m/s
6 s= 5 m/s2
Step 4 Plug-in the numbers.Solve.
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?
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Do the problems 8-9 on your notes.
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This brings up an important point. In common language,
when things speed up, we say that they are "accelerating,"
and, when they slow down, we say that they are "decelerating."
Any time an object's velocity is changing, we say that the
object is accelerating.
Acceleration is defined as the
change in velocity over time.
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However, in the language of physics, we say that
both objects are accelerating, not because both objects are speeding
up, but because both objects have changing
velocities.
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Velocity involves both speed and direction. Changing velocity does not have to necessarily involve a change in speed. It could just involve a change in direction.7
0 m
i/h
70 mi/h
70 mi/h
70 m
i/h
70 mi/h
70 mi/h
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Constant Speed Constant Speed of 55 mphof 55 mph
1. Consider a car moving at a constant speed of 55 mph while turning in a circle.
2. The car's velocity is not constant, even though the speed is constant.
3. WHY? This is because the direction of motion is constantly changing while the car is turning around the track.
4. Since the direction is changing, even though the speed is not, the velocity is changing (velocity involves both speed and direction).
Think Differently About AccelerationThink Differently About Acceleration
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Constant Speed Constant Speed of 55 mphof 55 mph 6. As a result, the car is accelerating,
even though it is neither speeding up nor slowing down.
5. The car is accelerating because its velocity is changing.
Think Differently About AccelerationThink Differently About Acceleration