Unit 3
Academic Physics
Name___________________
Speed and Velocity
Answer the following questions from chapter 2 in your textbook.
1. _________________ is a measure of how fast something is moving. Alternately, ____________ is
the rate at which distance is being covered.
2. The speed of a body at a specific instant in time is known as the _______________ _____________.
3. The equation below represents ________________ _________________. In this equation,
v represents ________________ _________________, d is the total distance covered, and t is the time
interval needed to cover that distance.
v
d 2 d1
t2 t1
4. ______________________ is the speed of a body in a given direction.
Identify each of the quantities below as either a speed, velocity or neither. Briefly explain why you
made your choice.
5. 35 km/h
Speed
Velocity
Neither
Why? ______________________________________________________________________________
6. 13 in/s down
Speed
Velocity
Neither
Why? ______________________________________________________________________________
7. 25.6 miles
Speed
Velocity
Neither
Why? ______________________________________________________________________________
8. 55 m/s
Speed
Velocity
Neither
Why? ______________________________________________________________________________
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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9. 12 m/s North
Speed
Velocity
Neither
Why? ______________________________________________________________________________
Given the known quantities below, find the unknown, desired quantity. Use the formulas above in order
to find the answers.
10. A dog runs 40.0 feet in 3 minutes. What is its average speed?
11. The average speed of a car is 55 mi/h (miles per hour). If the car drives for 3.5 hours, then how far
did it go?
12. In order to have a constant velocity we must have a constant speed and a constant ______________.
13. There are two ways that the velocity of a moving body can change. Name them below.
a. ________________________________________________________________
b. ________________________________________________________________
14. In the picture above, Dr. Physics is initially traveling at 10 m/s East. Is the underlined value a speed
or a velocity? Why?
15. As Dr. Physics begins to climb the ramp, what two components of his velocity change and how do
they change?
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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Constant Acceleration Graphs and Kinematics
16. Determine the acceleration of the body from the plot of its
graph shown to the right at the times requested.
`
15
a = _______________
b. t = 3 to 6 seconds:
a = _______________
c. t = 15 seconds:
a = _______________
d. t = 10 seconds:
Acceleration (m/s 2)
a. t = 2 seconds:
Acceleration
10
5
0
0
5
10
15
20
-5
a = _______________
-10
Tim e (s)
17. A train starts from rest and drives along a straight path. Its
Acceleration v. Time graph is shown to the left.
a. What is the speed of the train after accelerating for 13.0 s?
Acceleration
Acceleration (m/s 2)
12
10
8
6
4
2
0
0
10
WS 8 Problem 2
20
30
Tim e (s)
b. How far did the train go in 13.0 s?
Variable
a
v1
v2
d1
d2
t
v2
v2
v1
2
d2
v1
d1
Know
Want
at
2
2a d 2 d1
1 2
v1t
at
2
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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18. At 9:00 AM a train, which is 140.0 km West of the station, is traveling at a velocity of 92 km/hr
West. Where will the train be 5.0 hours later?
Variable
a
v1
v2
d1
d2
t
v2
v1
2
d2
v1
d1
Want
at
2
2a d 2 d1
1 2
v1t
at
2
19. The graph to the right shows the Velocity v. Time for a bike
rider.
a. What is the rider’s initial speed?
Velocity v. Time
15
Velocity (km/hr)
v2
Know
10
5
0
0
1
2
3
4
-5
b. What is the rider’s speed after 30.0 min?
Time (hr)
Ac Phy Unit 2 Exam
c. Using the kinematics equations below, calculate the acceleration of the bike in the first 30.0 min.
Variable
a
v1
v2
d1
d2
t
Know
v2
v2
2
v1
d2
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
2
Want
v1
2a d 2
d1 v1t
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at
d1
1 2
at
2
20. At 1300 you are in your tank traveling at 35.0 km/h East. Your base is 5.5 km West of your 1300
pm position. How far from your base will you be at 1400?
Variable
a
v1
v2
d1
d2
t
v2
v2
v1
2
d2
v1
d1
Know
Want
at
2
2a d 2 d1
1 2
v1t
at
2
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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Kinematics with Free Fall
21. At 5:30 pm, you are in a car traveling at 75.0 km/h West. Wal*mart is 8.0 km East of your 5:30 pm
position. How far from Wal*Mart will you be at 8:30 pm?
Variable Know Want
a
v1
v2
d1
d2
t
v2
v2
v1
2
d2
v1
at
2
d1
2a d 2 d1
1 2
v1t
at
2
22. A bullet is fired horizontally with an initial velocity of 800 m/s at a target located 200 m from the
rifle. How much time is required for the bullet to reach the target?
Variable Know Want
a
v1
v2
d1
d2
t
v2
v2
v1
2
d2
v1
d1
at
2
2a d 2 d1
1 2
v1t
at
2
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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23. Free fall: A steel ball is dropped from a diving platform (with an initial velocity of zero). Using
the value of a = g = - 9.8 m/s2, answer the following questions.
a. What is the velocity of the ball 1.2 seconds after its release?
Variable Know Want
a
v1
v2
d1
d2
t
v2
v2
2
d2
v1
v1
2
d1
at
2a d 2 d1
1 2
v1t
at
2
b. How far did it fall in 2.1 s?
Variable Know Want
a
v1
v2
d1
d2
t
v2
v2
2
d2
v1
v1
2
d1
at
2a d 2 d1
1 2
v1t
at
2
c. What is the velocity 2.4 seconds after its release?
Variable Know Want
a
v1
v2
d1
d2
t
v2
v2
2
d2
v1
v1
d1
2
at
2a d 2 d1
1 2
v1t
at
2
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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24. Use free fall to calculate the time it takes for the bail of hay to
hit the barn floor. The elevator is 3.5 m high.
Variable Know Want
a
v1
v2
d1
d2
t
v2
v2
2
d2
v1
v1
2
d1
at
2a d 2 d1
1 2
v1t
at
2
25. A helicopter drops a package from 175 m. Answer the following questions.
a. What is the final height of the package?
b. What is the initial downward velocity of the package?
d. How long does it take the package to land on the ground?
f. How fast is the package going when it hits the ground?
Variable Know Want
a
v1
v2
d1
d2
t
v2
v2
2
d2
v1
v1
d1
2
at
2a d 2 d1
1 2
v1t
at
2
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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26. A helicopter drops a package from 175 m while ascending at 32.5 m/s.
a. What is the initial velocity of the package?
b. How fast is the package going when it hits the ground?
c. How long does it take the package to land on the ground?
Variable Know Want
a
v1
v2
d1
d2
t
v2
v2
2
d2
v1
v1
d1
2
at
2a d 2 d1
1 2
v1t
at
2
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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Kinematics with Free Fall
27. Starting from rest, a car accelerates at a rate of 4.5 m/s for a time of 6 seconds. What is its velocity
at the end of this time?
Variable Know Want
a
v1
v2
d1
d2
t
v2
v2
v1
2
d2
v1
at
2
d1
2a d 2 d1
1 2
v1t
at
2
28. The velocity of a car decreases from 30 m/s to 12 m/s in a time of 4 seconds. What is the average
acceleration of the car in this process?
Variable Know Want
a
v1
v2
d1
d2
t
v2
v2
v1
2
d2
v1
d1
at
2
2a d 2 d1
1 2
v1t
at
2
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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29. A runner moving with an initial velocity of 9.0 m/s slows down at a constant rate of -1.5 m/s2 over a
period of 2 seconds.
a. What is her velocity at the end of this time?
Variable Know Want
a
v1
v2
d1
d2
t
v2
v2
2
d2
v1
v1
d1
2
at
2a d 2 d1
1 2
v1t
at
2
b. What distance does she travel during this process?
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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Free Fall
Displacement v. Time
A Potato is fired from a spud
mortar as shown. The spud
leaves the mortar barrel at a
height of +2.0 m above the
ground and at a velocity of +13
m/s.
12
Distance (m)
10
8
6
4
2
0
0
0.5
1
1.5
2
Answer the following questions
below.
2.5
Time (s)
30. What does the “+” mean when attached to the
velocity and the initial height?
Velocity v. Time
15
Velocity (m/s)
10
31. What is the value of the acceleration (magnitude
and direction) acting on the potato once it has left the
mortar?
5
0
-5
0
0.5
1
1.5
2
2.5
-10
-15
-20
Time (s)
32. How would I express this acceleration in
“mathematical form?”
33. Calculate the displacement and the velocity of the potato at the time intervals shown below.
Variable 0 s
a
v1
v2
d1
d2
v2
v2
v1
2
d2
v1
d1
0.5 s
1.0 s
1.5 s
2.0 s
2.5 s
2.8 s
at
2
2a d 2 d1
1 2
v1t
at
2
34. Plot the Displacement v. Time and Velocity v. Time calculated in number four on the graphs at the
top of page 1.
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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Graphical analysis.
35. What was the maximum height reached by the potato?
____________________________________________________________________________________
36. At what time did the potato reach its maximum height? Justify your answer.
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
37. What was the velocity of the potato at its maximum height? Explain your answer.
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
38. At what time(s) was the potato 6.0 m above the ground?
____________________________________________________________________________________
39. What was the velocity of the potato at each of the times above?
____________________________________________________________________________________
____________________________________________________________________________________
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40. A physics book is moved once around the perimeter of a rectangular
table of dimensions 1.0m by 2.0m. If the book ends up at its initial position,
what is its displacement from start to finish?
41. What is the total distance traveled by the book?
A position-time graph (d vs. t) represents the motion of an object for 90s. Use the position-time graph to
find the distance the object travels between the intervals. In addition, find the object’s displacement
during these intervals.
Position vs. Time Graph
Distance
(m)
Displacement
(m)
Position (m)
500
Time Interval
(s)
0s to 30s
30s to 60s
60s to 75s
75s to 90s
400
300
200
100
0
0
10
20
30
40
50
60
70
80
90
Time (s)
42. You and a friend each drive 50km. You travel at 90km/h and your friend travels at 95km/h. How
long will your friend wait for you at the end of the trip?
You
Variable
Know
d1
d2
t1
t2
v
Your Friend
Variable
Know
d1
d2
t1
t2
v
Want
Want
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved. Unit 3
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*** Giancoli Physics Homework Assignment ***
Read Chapter 2 Sections 5-7
Answer Conceptual Questions (Page 38) 8, 11, 13, & 19.
Do Problems (Page 40) 21, 25, 28, and 33.
Chapter Vocabulary
Unit 2 Vocabulary applies to Unit 3.
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