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AP Physics C: One Dimensional Kinematics
Multiple Choice Questions
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1
In the absence of air resistance, a ball dropped near
the surface of the Earth experiences a constant
acceleration of 9.8 m/s2. This means that the
A Speed of the object increases 9.8 m/s during each second.
B
speed of the object as it falls is 9.8 m/s
C object falls 9.8 meters during each second
D object falls 9.8 meters during the first second only
derivative of the distance with respect to time for the object
E equals 9.8 m/s squared
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2
A 1000-kilogram truck accelerates uniformly from rest,
reaching a speed of 50 meters per second in 10
seconds. During the 10 seconds, the car has traveled
a distance of
A 85 m
B
175 m
C 200 m
D 250 m
E
300 m
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3
The graph above shows the velocity v as a function of
time t for an object moving in a straight line. Which of
the following graphs shows the corresponding
displacement x as a function of time t for the same time
interval?
A
E
C
DB
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4 At tim e t = 0, car A traveling with speed v0 passes car B. which is just starting to m ove. Both cars
then travel on two parallel lanes of the sam e straight road. The graphs of speed v versus tim e t
for both cars are shown above.
Which of the following is true at tim e t = 10 seconds?
A
Car B is behind car A
B
Car B is passing car A
C
Car B is in front of car A
D
Both cars have the sam e acceleration
E
Car B is accelerating fester then car A
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5 At tim e t = 0, car A traveling with speed v0 passes car B. which is just starting to m ove. Both cars
then travel on two parallel lanes of the sam e straight road. The graphs of speed v versus tim e t
for both cars are shown above.
From tim e t = 0 to tim e t = 20 seconds, the areas under both curves are equal. Therefore, which
of the following is true at tim e t = 20 seconds?
A
Car B is behind car A
B
Car B is passing car A
C
Car B is in front of car A
D
Both cars have the sam e acceleration
E
Car B is accelerating faster than car A
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6 A runner m oving in the + x direction passes the origin at tim e t = 0. Between t
= 0 and t = 2 seconds, the runner has a constant speed of 8 m / s and at t = 2
seconds is accelerating at a constant rate of 4 m / s2 in the - x direction. The
distance where the runner is located at t = 5 seconds is
A
+ 14 m
B
+ 94 m
C
+ 22 m
D
- 74 m
E
- 94 m
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7 Which of the following pairs of graphs shows the distance traveled versus tim e and the speed
versus tim e for an object uniform ly decelerating to rest?
A
B
D
C
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8 A particle m oves along the x - ax is with a non- constant acceleration described by a = 6t, where a i
in m eters per second squared and t is in seconds. If the particle starts from rest so that its
speed v and position x are zero when t = 0, where is it located when t = 2 seconds?
A
x = 4m
B
x = 8m
C
x = 16 m
D
x = 24 m
E
x = 36 m
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Questions 9- 10
9 An object m oving in a straight line has a velocity v in m eters per second that varies with tim e t in
seconds according to the following function.
v = 8 + 2.5 t 2
The instantaneous acceleration of the object at t = 2 seconds is
A
2 m / s2
B
4 m/ s
2
C
6 m/ s
2
D
8 m/ s
E
10 m / s2
2
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Questions 9- 10
10 An object m oving in a straight line has a velocity v in m eters per second that varies with tim e t in
seconds according to the following function.
v = 8 + 2.5 t 2
The displacem ent of the object between t = 0 and t = 6 seconds is
A
120 m
B
180 m
C
228 m
D
242 m
E
260 m
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11 A rocket is shot vertically upward into the air with a positive initial velocity. Which of the
following correctly describes the velocity and acceleration of the object at its m ax im um
elevation?
Velocity
Acceleration
A
Positive
Negative
B
Zero
Zero
C
Negative
Negative
D
Zero
Negative
E
Positive
Positive
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Questions 12- 15
The acceleration of an object is given by the function: a= 8t+ 4 for all values of t> 0.
The object is initially 2 m eters from the origin and m oving to the right with a
speed of 2 m eters per second.
12 Find the velocity at t = 3 seconds
A
37 m / s
B
43 m / s
C
50 m / s
D
62 m / s
E
78 m / s
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Questions 12- 15
The acceleration of an object is given by the function: a= 8t+ 4 for all values of t> 0.
The object is initially 2 m eters from the origin and m oving to the right with a
speed of 2 m eters per second.
13 Find the instantaneous speed of the object at t = 2 seconds
A
12 m / s
B
26 m / s
C
33 m / s
D
41 m / s
E
50 m / s
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Questions 12- 15
The acceleration of an object is given by the function: a= 8t+ 4 for all values of t> 0.
The object is initially 2 m eters from the origin and m oving to the right with a
speed of 2 m eters per second.
14 Find the total distance traveld at t = 3 by the object
A
48 m
B
56 m
C
62 m
D
66 m
E
72 m
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Questions 12- 15
The acceleration of an object is given by the function: a= 8t+ 4 for all values of t> 0.
The object is initially 2 m eters from the origin and m oving to the right with a
speed of 2 m eters per second.
15 Find the displacem ent of the object at t = 2 seconds
A
15 m
B
20 m
C
25m
D
30 m
E
35 m
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16 An object in free fall has a velocity of 5 m eters per second in the upward direction. What is the
instantaneous velocity of the object one second later?
A
10 m / s down
B
5 m / s up
C
10 m / s up
D
5 m / s down
E
14 m / s down
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17 At what speed should an object be launched at in order to achieve a height of 20 m ?
A
10 m / s
B
14 m / s
C
20 m / s
D
23 m / s
E
29 m / s
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18 How long m ust a 5 m / s2 acceleration act to change the velocity of a 5 kg object by 6 m / s?
A
0.6 m / s
B
1.2 m / s
C
2.4 m / s
D
3.6 m / s
E
4.8 m / s
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19 An object is thrown straight downward on Earth with an initial speed of 10 m / s from a position
of 20 m eters above the ground. Ignoring air resistance the speed of the object when it reaches
the ground is about
A
13.2 m / s
B
16.1 m / s
C
19.5 m / s
D
22.2 m / s
E
31.7 m / s
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20 A ball initially at rest falls a height h without air resistance. If the ball falls a distance of h/ 2 in a
tim e t, how m uch tim e is required to fall the rem aining h/ 2?
A
0.25 t
B
0.4 t
C
0.5 t
D
0.71 t
E
1t
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Questions 21- 26
The following function represents the path taken by an object:
x = 4t 2 - 3t+ 2 where x is the object’s displacem ent and t is tim e.
The object starts at x = 2 m eters away from the origin and accelerates from rest.
21 How far does the object travel at t = 3 if the object starts at t = 0?
A
16 m
B
23 m
C
27 m
D
33 m
E
39 m
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Questions 21- 26
The following function represents the path taken by an object:
x = 4t 2 - 3t+ 2 where x is the object’s displacem ent and t is tim e.
The object starts at x = 2 m eters away from the origin and accelerates from rest.
22 How far away from the origin is the object at t = 4?
A
42 m
B
54 m
C
56 m
D
60 m
E
68 m
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Questions 21- 26
The following function represents the path taken by an object:
x = 4t 2 - 3t+ 2 where x is the object’s displacem ent and t is tim e.
The object starts at x = 2 m eters away from the origin and accelerates from rest.
23 What is the instantaneous speed of the object at t = 2?
A
13 m / s
B
18 m / s
C
23 m / s
D
28 m / s
E
33 m / s
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Questions 21- 26
The following function represents the path taken by an object:
x = 4t 2 - 3t+ 2 where x is the object’s displacem ent and t is tim e.
The object starts at x = 2 m eters away from the origin and accelerates from rest.
24 At what tim e is the velocity of the object about 29 m eters per second?
A
2s
B
4s
C
5s
D
6s
E
8s
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Questions 21- 26
The following function represents the path taken by an object:
x = 4t 2 - 3t+ 2 where x is the object’s displacem ent and t is tim e.
The object starts at x = 2 m eters away from the origin and accelerates from rest.
25 What is the instantaneous acceleration of the object at t = 3?
A
8 m / s^ 2
B
12 m / s^ 2
C
20 m / s^ 2
D
24 m / s^ 2
E
none (velocity is constant)
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Questions 21- 26
The following function represents the path taken by an object:
x = 4t 2 - 3t+ 2 where x is the object’s displacem ent and t is tim e.
The object starts at x = 2 m eters away from the origin and accelerates from rest.
26 At what tim e is the acceleration of the object about 10 m / s^ 2?
A
0s
B
2s
C
4s
D
8s
E
at no tim e is the acceleration 10 m / s^ 2
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Questions 27-30
The acceleration of an object is represented by the function a = 9t 2 + 2 for t> 0.
At t= 0 the object at x = - 2 m and is traveling with a velocity of 3 m eters per second
in the negative x direction.
27 How fast is the object m oving at t = 2?
A
13 m / s
B
25 m / s
C
38 m / s
D
47 m / s
E
none (velocity is zero)
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Questions 27-30
The acceleration of an object is represented by the function a = 9t 2 + 2 for t> 0.
At t= 0 the object at x = - 2 m and is traveling with a velocity of 3 m eters per second
in the negative x direction.
28 What is the instataneous acceleration at t = 3?
A
9 m / s^ 2
B
19 m / s^ 2
C
41 m / s^ 2
D
54 m / s^ 2
E
83 m / s^ 2
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Questions 27-30
The acceleration of an object is represented by the function a = 9t 2 + 2 for t> 0.
At t= 0 the object at x = - 2 m and is traveling with a velocity of 3 m eters per second
in the negative x direction.
29 At what tim e is the acceleration approx im ately 26 m / s^ 2?
A
1s
B
2s
C
3s
D
4s
E
nonw (there is no tim e in which acceleration is 36 m / s^ 2
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Questions 27-30
The acceleration of an object is represented by the function a = 9t 2 + 2 for t> 0.
At t= 0 the object at x = - 2 m and is traveling with a velocity of 3 m eters per second
in the negative x direction.
30 How far from the origin is the object at t = 2?
A
8m
B
14 m
C
26 m
D
28 m
E
37 m
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Question 31- 32
A car starting from rest uniform ly accelerates in a straight line as shown above
31 What was the acceleration during the entire 3 second interval?
(t 0 = 0s, x 0 = 0m ; t 1 = 1s, x 1 = 2m ; t 2 = 2s, x 2 = 8m ; t 3 = 3s, x 3 = 18m )
A
1 m / s^ 2
B
3 m / s^ 2
C
4 m / s^ 2
D
6 m / s^ 2
E
12 m / s^ 2
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Question 31- 32
A car starting from rest uniform ly accelerates in a straight line as shown above
32 What was the average velocity of the car during the first two seconds?
(t 0 = 0s, x 0 = 0m ; t 1 = 1s, x 1 = 2m ; t 2 = 2s, x 2 = 8m ; t 3 = 3s, x 3 = 18m )
A
2 m/ s
B
4 m/ s
C
6 m/ s
D
8 m/ s
E
10 m / s