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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

Ederivative of the distance with respect to time for the object 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?

ABCDE

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4 At t ime t = 0, car A traveling with speed v0 passes car B. which is just start ing to move. Both cars then travel on two parallel lanes of the same straight road. The graphs of speed v versus t ime t for both cars are shown above.

Which of the following is true at t ime 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 same accelerat ion

E Car B is accelerat ing fester then car A

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5 At t ime t = 0, car A traveling with speed v0 passes car B. which is just start ing to move. Both cars then travel on two parallel lanes of the same straight road. The graphs of speed v versus t ime t for both cars are shown above.From t ime t = 0 to t ime t = 20 seconds, the areas under both curves are equal. Therefore, which of the following is true at t ime 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 same accelerat ion

E Car B is accelerat ing faster than car A

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6 A runner moving in the + x direct ion passes the origin at t ime 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 accelerat ing at a constant rate of 4 m/ s2 in the - x direct ion. 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 t ime and the speed versus t ime for an object uniformly decelerat ing to rest?

A B

CD

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8 A part icle moves along the x- ax is with a non- constant accelerat ion described by a = 6t, where a is in meters per second squared and t is in seconds. If the part icle starts from rest so that its speed v and posit ion x are zero when t = 0, where is it located when t = 2 seconds?

A x = 4 m

B x = 8 m

C x = 16 m

D x = 24 m

E x = 36 m

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9 An object moving in a straight line has a velocity v in meters per second that varies with t ime t in seconds according to the following funct ion. v = 8 + 2.5 t2

The instantaneous accelerat ion of the object at t = 2 seconds is

A 2 m/ s2

B 4 m/ s2

C 6 m/ s2

D 8 m/ s2

E 10 m/ s2

Quest ions 9- 10

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10 An object moving in a straight line has a velocity v in meters per second that varies with t ime t in seconds according to the following funct ion. v = 8 + 2.5 t2

The displacement 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

Quest ions 9- 10

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11 A rocket is shot vert ically upward into the air with a posit ive init ial velocity. Which of the following correct ly describes the velocity and accelerat ion of the object at its maximum elevat ion?

A

B

C

D

E

Velocity Accelerat ion

Positive Negative

Zero Zero

Negative Negative

Zero Negative

Positive Positive

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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

Quest ions 12- 15The accelerat ion of an object is given by the funct ion: a= 8t+ 4 for all values of t> 0. The object is init ially 2 meters from the origin and moving to the right with a speed of 2 meters per second.

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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

Quest ions 12- 15The accelerat ion of an object is given by the funct ion: a= 8t+ 4 for all values of t> 0. The object is init ially 2 meters from the origin and moving to the right with a speed of 2 meters per second.

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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

Quest ions 12- 15The accelerat ion of an object is given by the funct ion: a= 8t+ 4 for all values of t> 0. The object is init ially 2 meters from the origin and moving to the right with a speed of 2 meters per second.

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15 Find the displacement of the object at t = 2 seconds

A 15 m

B 20 m

C 25m

D 30 m

E 35 m

Quest ions 12- 15The accelerat ion of an object is given by the funct ion: a= 8t+ 4 for all values of t> 0. The object is init ially 2 meters from the origin and moving to the right with a speed of 2 meters per second.

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16 An object in free fall has a velocity of 5 meters per second in the upward direct ion. 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 must a 5 m/ s2 accelerat ion 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 init ial speed of 10 m/ s from a posit ion of 20 meters 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 init ially at rest falls a height h without air resistance. If the ball falls a distance of h/ 2 in a t ime t , how much t ime is required to fall the remaining h/ 2?

A 0.25 t

B 0.4 t

C 0.5 t

D 0.71 t

E 1 t

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21 How far does the object t ravel 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

Quest ions 21- 26The following funct ion represents the path taken by an object: x= 4t2- 3t+ 2 where x is the object ’s displacement and t is t ime. The object starts at x= 2 meters away from the origin and accelerates from rest.

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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

Quest ions 21- 26The following funct ion represents the path taken by an object: x= 4t2- 3t+ 2 where x is the object ’s displacement and t is t ime. The object starts at x= 2 meters away from the origin and accelerates from rest.

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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

Quest ions 21- 26The following funct ion represents the path taken by an object: x= 4t2- 3t+ 2 where x is the object ’s displacement and t is t ime. The object starts at x= 2 meters away from the origin and accelerates from rest.

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24 At what t ime is the velocity of the object about 29 meters per second?

A 2 s

B 4 s

C 5 s

D 6 s

E 8 s

Quest ions 21- 26The following funct ion represents the path taken by an object: x= 4t2- 3t+ 2 where x is the object ’s displacement and t is t ime. The object starts at x= 2 meters away from the origin and accelerates from rest.

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25 What is the instantaneous accelerat ion 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)

Quest ions 21- 26The following funct ion represents the path taken by an object: x= 4t2- 3t+ 2 where x is the object ’s displacement and t is t ime. The object starts at x= 2 meters away from the origin and accelerates from rest.

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26 At what t ime is the accelerat ion of the object about 10 m/ s^ 2?

A 0 s

B 2 s

C 4 s

D 8 s

E at no t ime is the accelerat ion 10 m/ s^ 2

Quest ions 21- 26The following funct ion represents the path taken by an object: x= 4t2- 3t+ 2 where x is the object ’s displacement and t is t ime. The object starts at x= 2 meters away from the origin and accelerates from rest.

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27 How fast is the object moving at t = 2?

A 13 m/ s

B 25 m/ s

C 38 m/ s

D 47 m/ s

E none (velocity is zero)

Quest ions 27-30 The accelerat ion of an object is represented by the funct ion a = 9t2+ 2 for t> 0. At t= 0 the object at x= - 2 m and is traveling with a velocity of 3 meters per second in the negat ive x direct ion.

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28 What is the instataneous accelerat ion 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

Quest ions 27-30 The accelerat ion of an object is represented by the funct ion a = 9t2+ 2 for t> 0. At t= 0 the object at x= - 2 m and is traveling with a velocity of 3 meters per second in the negat ive x direct ion.

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29 At what t ime is the accelerat ion approx imately 26 m/ s^ 2?

A 1 s

B 2 s

C 3 s

D 4 s

E nonw (there is no t ime in which accelerat ion is 36 m/ s^ 2

Quest ions 27-30 The accelerat ion of an object is represented by the funct ion a = 9t2+ 2 for t> 0. At t= 0 the object at x= - 2 m and is traveling with a velocity of 3 meters per second in the negat ive x direct ion.

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30 How far from the origin is the object at t = 2?

A 8 m

B 14 m

C 26 m

D 28 m

E 37 m

Quest ions 27-30 The accelerat ion of an object is represented by the funct ion a = 9t2+ 2 for t> 0. At t= 0 the object at x= - 2 m and is traveling with a velocity of 3 meters per second in the negat ive x direct ion.

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31 What was the accelerat ion during the ent ire 3 second interval?(t0= 0s, x 0= 0m; t1= 1s, x 1= 2m; t2= 2s, x 2= 8m; t3= 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

Quest ion 31- 32

A car start ing from rest uniformly accelerates in a straight line as shown above

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32 What was the average velocity of the car during the f irst two seconds?(t0= 0s, x 0= 0m; t1= 1s, x 1= 2m; t2= 2s, x 2= 8m; t3= 3s, x 3= 18m)

A 2 m/ s

B 4 m/ s

C 6 m/ s

D 8 m/ s

E 10 m/ s

Quest ion 31- 32

A car start ing from rest uniformly accelerates in a straight line as shown above