# Kinematics 66 Multiple Choice Questions

45

## Full text

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1. The graph shows the variation with time t of the velocity v of an object. v

t

Which one of the following graphs best represents the variation with time t of the acceleration a of the object?

0 0

0 0

0 0

0 0

a a

a a

t t

t t

A . B .

C . D .

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2. A ball, initially at rest, takes time t to fall through a vertical distance h. If air resistance is

ignored, the time taken for the ball to fall from rest through a vertical distance 9h is

A. 3t.

B. 5t.

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3. A raindrop falling through air reaches a terminal velocity before hitting the ground. At terminal velocity, the frictional force on the raindrop is

A. zero.

B. less than the weight of the raindrop.

C. greater than the weight of the raindrop.

D. equal to the weight of the raindrop.

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4. The diagram below shows the path of a projectile in the absence of air resistance.

V e r t i c a l p o s i t i o n

H o r i z o n t a l p o s i t i o n

Which one of the following diagrams best represents the path of the projectile under the same initial conditions when the air resistance is taken into account? (The path in absence of air resistance is shown for comparison as a dotted line.)

V e r t i c a l

p o s i t i o n V e r t i c a lp o s i t i o n

V e r t i c a l

p o s i t i o n V e r t i c a lp o s i t i o n

H o r i z o n t a l p o s i t i o n H o r i z o n t a l p o s i t i o n

A . B .

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5. A sailing boat is moving with constant velocity v to the right parallel to the dock.

Sailor Hulot, up on the mast, drops his telescope at the moment he is opposite Lucie who is standing on the dock. Which one of the following best shows the path of the falling telescope as seen by Lucie?

A . B .

C . D .

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6. An athlete runs round a circular track at constant speed. Which one of the following graphs best represents the variation with time t of the magnitude d of the displacement of the athlete from the starting position during one lap of the track?

d d d d 0 0 0 0 0 0 0 0 t t t t A . C . B . D . (1)

7. A ball is released from rest near the surface of the Moon. Which one of the following quantities

increases at a constant rate?

A. Only distance fallen

B. Only speed

C. Only speed and distance fallen

D. Only speed and acceleration

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8. A stone is thrown horizontally from the top of a high cliff. Assuming air resistance is negligible, what is the effect of gravitational force on the horizontal and on the vertical components of the velocity of the stone?

Vertical component of velocity Horizontal component of velocity

A. increases to a constant value stays constant

B. increases continuously stays constant

C. increases to a constant value decreases to zero

D. increases continuously decreases to zero

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9. A car is heading due East at a speed of 10 m s−1. A bird is flying due North at a speed of 4 m s−1,

as shown below.

N

S E W

B i r d 1 0 m s

4 m s

C a r

– 1

– 1

Which one of the following vectors represents the velocity of the bird relative to a person in the car?

A .

C .

B .

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10. A stone is thrown from O at an angle to the horizontal. Which sketch below best shows the path of the stone when air resistance is not neglected? On each sketch, the broken line shows the path for the same stone in a vacuum.

A .

C .

B .

D . O

O

O

O

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11. Peter and Susan both stand on the edge of a vertical cliff.

V ( P e t e r )

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Susan throws a stone vertically downwards and, at the same time, Peter throws a stone vertically upwards. The speed V with which both stones are thrown is the same. Neglecting air resistance, which one of the following statements is true?

A. The stone thrown by Susan will hit the sea with a greater speed than the stone thrown by

Peter.

B. Both stones will hit the sea with the same speed no matter what the height of the cliff.

C. In order to determine which stone hits the sea first, the height of the cliff must be known.

D. In order to determine which stone hits the sea first both the height of the cliff and the mass

of each stone must be known.

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12. A ball is dropped from rest at time t = 0 on to a horizontal surface from which it rebounds. The

graph shows the variation of time t with speed v of the ball.

0 0 B D

A C v

t

Which one of the following best represents the point at which the ball just loses contact with the surface after the first bounce?

A. A

B. B

C. C

D. D

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13. Juan is standing on the platform at a railway station. A train passes through the station with

speed 20 m s–1 in the direction shown measured relative to the platform. Carmen is walking

along one of the carriages of the train with a speed of 2.0 m s–1 measured relative to the carriage

in the direction shown. Velocity is measured as positive in the direction shown on the diagram.

J u a n C a r m e n

p l a t f o r m 2 . 0 m s

2 0 m s

v e l o c i t y m e a s u r e d a s a p o s i t i v e i n t h i s d i r e c t i o n

– 1 – 1

The velocity of Carmen relative to Juan is

A. –22 m s–1.

B. –18 m s–1.

C. +18 m s–1.

D. +22 m s–1.

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14. A ball is dropped from rest at time t = 0 on to a horizontal surface from which it rebounds. Which one of the following graphs best shows the variation of speed v of the ball with time t from the time t = 0 to the time that the ball leaves the surface?

0 0 0 0 v v v v 0 0 0 0 t t t t A . C . B . D . (1)

15. Which one of the following is a true statement concerning the vertical component of the velocity

and the acceleration of a projectile when it is at its maximum height? (The acceleration of free fall is g.)

Vertical component of velocity Acceleration

A. maximum zero

B. maximum g

C. zero zero

D. zero g

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16. The diagram below shows the variation with time t of the velocity v of an object. v

t 0

0

The area between the line of the graph and the time-axis represents

A. the average velocity of the object.

B. the displacement of the object.

C. the impulse acting on the object.

D. the work done on the object.

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17. The diagram below shows the variation with time t of the velocity v of an object.

v

t 0

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Which one of the following graphs shows the variation with time t of the acceleration a of the object?

a

a

a

a t

t

t

t 0

0

0

0 0

0

0

0 A .

C .

B .

D .

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18. A stone X is thrown vertically upwards with speed v from the top of a building. At the same

time, a second stone Y is thrown vertically downwards with the same speed v as shown.

B u i l d i n g

X Y

v

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Air resistance is negligible. Which one of the following statements is true about the speeds with which the stones hit the ground at the base of the building?

A. The speed of stone X is greater than that of stone Y.

B. The speed of stone Y is greater than that of stone X.

C. The speed of stone X is equal to that of stone Y.

D. Any statement about the speeds depends on the height of the building.

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19. The graph below shows the variation with time of the distance moved by a car along a straight

road. During which time interval does the car have its greatest acceleration?

A B C D

d i s t a n c e m o v e d

t i m e

(1)

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The minute hand is observed at the time shown above and then again, 30 minutes later. What is the displacement of, and the distance moved by, the end P of the minute hand during this time interval?

displacement distance moved

A. 2L vertically downwards πL

B. 2L vertically upwards πL

C. 2L vertically downwards 2L

D. 2L vertically upwards 2L

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21. A ball is thrown horizontally from the top of a cliff. Air resistance is negligible. Which of the

following diagrams best represents the subsequent path of the ball? A .

C .

B .

D .

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22. Which one of the following is a correct definition of displacement?

A. Distance from a fixed point

B. Distance moved from a fixed point

C. Distance from a fixed point in a given direction

D. Distance moved in a given direction

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23. The variation with time t of the speed v of a car moving along a straight road is shown below.

v

t 0

0

S1 S2 S3

Which area, S1, S2 or S3, or combination of areas, represents the total distance moved by the car

during the time that its speed is reducing?

A. S1

B. S3

C. S1 + S3

D. S1 + S2 + S3

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24. A ball is held at rest in air. The ball is then released. Which one of the following graphs best shows the variation with time t of the distance d fallen by the ball?

A . C . B . D . d d d d t t t t 0 0 0 0 0 0 0 0 (1)

25. A boy throws a small stone at an angle to the horizontal.

Which one of the following sketches best shows the path of the stone as it rises and then falls back to Earth? Air resistance is negligible and the acceleration of free fall is constant.

A .

C .

B .

D .

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26. A car accelerates uniformly from rest. It then continues at constant speed before the brakes are applied, bringing the car to rest.

Which of the following graphs best shows the variation with time t of the acceleration a of the car?

a

a

a

a 0

0

0

0 0

0

0

0

t

t

t

t A .

B .

C .

D .

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27. Four cars W, X, Y and Z are on a straight road. The graph below shows the variation with time t of the distance s of each car from a fixed point.

s

t X

Y

Z W

0 0 Which car has the greatest speed?

A. W

B. X

C. Y

D. Z

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28. A stone is thrown at an angle to the horizontal. Ignoring air resistance, the horizontal component

of the initial velocity of the stone determines the value of

A. range only.

B. maximum height only.

C. range and maximum height.

D. range and time of flight.

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29. The graph below shows the variation with time t of the acceleration a of a spaceship.

### t

The spaceship is at rest at t = 0. The shaded area represents

A. the distance travelled by the spaceship between t = 0 and t = T.

B. the speed of the spaceship at t = T.

C. the rate at which the speed of the spaceship changes between t = 0 and t = T.

D. the rate at which the acceleration changes between t = 0 and t = T.

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30. A particle moves from a point P to a point Q in a time T. Which one of the following correctly

defines both the average velocity and average acceleration of the particle?

Average velocity Average acceleration

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31. Two stones, X and Y, of different mass are dropped from the top of a cliff. Stone Y is dropped a short time after stone X. Air resistance is negligible.

Whilst the stones are falling, the distance between them will

A. decrease if the mass of Y is greater than the mass of X.

B. increase if the mass of X is greater than the mass of Y.

C. decrease whether the mass of X is greater or less than the mass of Y.

D. increase whether the mass of X is greater or less than the mass of Y.

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32. The graph below shows the variation with time t of the acceleration a of a spaceship.

### t

The spaceship is at rest at t = 0. The shaded area represents

A. the distance travelled by the spaceship between t = 0 and t = T.

B. the speed of the spaceship at t = T.

C. the rate at which the speed of the spaceship changes between t = 0 and t = T.

D. the rate at which the acceleration changes between t = 0 and t = T.

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33. A stone is projected horizontally from the top of a cliff. Neglecting air resistance, which one of the following correctly describes what happens to the horizontal component of velocity and to the vertical component of velocity?

Horizontal component of velocity Vertical component of velocity

A. Decreases Increases

B. Decreases Constant

C. Constant Constant

D. Constant Increases

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34. A boat is moving in the direction shown with a speed of 5 m s−1 as measured by Nico who is at

rest on the beach. Aziz walks along the deck of the boat in the direction shown with a speed of 2

m s−1 measured relative to the boat.

p o s i t i v e d i r e c t i o n A z i z

5 m s– 1

N i c o

If velocity is measured as positive in the direction shown, the velocity of Nico relative to Aziz is

A. − 7 m s−1.

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35. The graph below shows the variation with time t of the displacement s of a car. In which time interval is the speed greatest?

s

0

0 A B C D t

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36. Two points P and Q are at distances r and 2r respectively from the centre of a compact disc (CD)

as shown.

P r

2 r Q

When the disc is rotating about its centre, the ratio of the

A. .

2 1

B. 1.

C.

### .

D. 2.

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37. An archer shoots an arrow at an angle to the horizontal. Air resistance is negligible. Which of the following graphs best represents the variation with time of the horizontal component of the arrow’s velocity from the time it is launched to the time just before it hits the ground?

A . v e l o c i t y

0

B . v e l o c i t y

0 0 t i m e

0 t i m e

C . v e l o c i t y

0

D . v e l o c i t y

0

0 t i m e 0 t i m e

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38. A ball is thrown vertically upwards from the ground. The graph shows the variation with time t of the vertical displacement d of the ball.

d

D

0

0 T t

Which one of the following gives the final displacement after time T and the average speed between time t = 0 and time t = T?

Displacement Average speed

A. 0 0

B. 0

T D

2

C. 2D

T D

2

D. 2D 0

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39. Points P and Q are at distances R and 2R respectively from the centre X of a disc, as shown below.

Q

P 2 R

R X

The disc is rotating about an axis through X, normal to the plane of the disc. Point P has linear speed v and centripetal acceleration a. Which one of the following is correct for point Q?

Linear speed Centripetal acceleration

A. v a

B. v 2a

C. 2v 2a

D. 2v 4a

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40. The graph below shows how a quantity y varies with time t for a falling object. y

0

0 t

Which one of the following quantities could be represented by y?

A. Speed when air resistance is negligible

B. Speed when air resistance is not negligible

C. Distance moved from rest when air resistance is negligible

D. Distance moved from rest when air resistance is not negligible

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41. A stone is thrown with speed v from the top of a cliff of height H, as shown below.

h v

c l i f f

H

s e a

The stone is thrown at an angle to the horizontal so that it rises to a height h above the top of the cliff before falling into the sea. The acceleration of free fall is g. Air resistance is negligible. Which one of the following expressions gives correctly the speed of the stone as it hits the sea?

A.

B.

C.

D.

v22gH

## 

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42. A ball is thrown vertically upwards at time t = 0. Air resistance is not negligible and the

acceleration of free fall is g. The ball reaches a maximum height at time t = T and then descends, reaching a terminal speed.

Which graph best shows the variation with time t of the acceleration a of the ball?

A . a

g

0

0 T t

B . a

g

0

0 T t

C . a

g

0

– g

0 T t

D . a

g

0

0 T t

– g – g

– g

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43. The graph below shows the variation with time t of the displacement d of a body moving along a straight-line.

d

0

0 t

Which graph best represents the variation with time t of the velocity v of this body?

A . v

0

B . v

0

0 t 0 t

C . v

0

D . v

0

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44. A body starting from rest moves along a straight-line under the action of a constant force. After travelling a distance d the speed of the body is v.

i n i t i a l p o s i t i o n

d

v

The speed of the body when it has travelled a distance

2

d

from its initial position is

A. .

4 v

B. .

2 v

C. .

2 v

D. .

2 2

v

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45. A ball rolls off a horizontal table with velocity v. It lands on the ground a time T later at a distance D from the foot of the table as shown in the diagram below. Air resistance is negligible.

v

t a b l e

D

A second heavier ball rolls off the table with velocity v. Which one of the following is correct for the heavier ball?

Time to land Distance from table

A. T D

B. T less than D

C. less than T D

D. less than T less than D

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46. The graph shows the variation with time t of the acceleration a of an object.

0 2 0

1 5

1 0

5 a / m s – 2

0 1 2 3 4 5 6 7 8 9 1 0

t / s The object is at rest at time t = 0.

Which of the following is the velocity of the object at time t = 6.0 s?

A. 0.50 m s–1.

B. 2.0 m s–1.

C. 36 m s–1.

D. 72 m s–1.

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47. An object is dropped from rest from a point several hundred metres above the surface of the Earth at time t = 0. The object strikes the ground at t = T and air resistance is not negligible. Which of the following sketch graphs best shows the variation with time t, of the speed v of the object?

B .

D . A .

C .

T t

T T

T

t t

t v

v v

v

0

0 0 0

0

0

0 0

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48. Which of the following is a correct definition of average acceleration? A. taken time y in velocit change B. taken time velocity C. taken time speed in change D. taken time speed (1)

49. A projectile is fired from the ground at time t = 0. It lands back on the ground at time t = T.

Which of the following sketch graphs best shows the variation with time t of the vertical speed

VV and horizontal speed VH of the projectile? Air resistance is negligible.

s p e e d s p e e d

s p e e d s p e e d

T

T t 0 t

0

0 0

A . B .

C . D .

VH

VH

VH VH

VV

VV

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50. An object has initial speed u and acceleration a. After travelling a distance s, its final speed is v. The quantities u, v, a and s are related by the expression

v2 = u2 + 2as.

Which of the following includes the two conditions necessary for the equation to apply?

A. a has constant direction u and v are in the same direction B. a has constant direction a, u and v are in the same direction

C. a has constant magnitude a has constant direction

D. a has constant magnitude u and v are in the same direction

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51. Two forces P and Q act at a point X. The individual forces are represented in magnitude and direction in the diagram below.

Which of the following diagrams best shows the value of S, where S = (P – Q)?

P

P P

P Q

Q

Q

Q S

S S

S

A . B .

C . D .

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52. Two identical metal spheres X and Y are released at the same time from the same height above the horizontal ground. Sphere X falls vertically from rest. Sphere Y is projected horizontally as shown below.

g r o u n d

X Y

Air resistance is negligible.

Which of the following statements is correct?

A. Sphere X hits the ground before sphere Y because it travels a shorter distance.

B. Sphere Y hits the ground before sphere X because its initial velocity is greater.

C. The spheres hit the ground at the same time because horizontal motion does not affect

vertical motion.

D. The spheres hit the ground at the same time because they have equal weights.

(1)

53. The graph below shows the variation with time t of the displacement s of an object moving along

a straight-line.

s / m

2 0 . 0

0 . 0

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54. The graph below shows the variation with time t of the acceleration a of a body moving in a straight-line.

a

0

0 t1 t2 t

A. the change in velocity from t1 to t2.

B. the velocity at t2.

C. the average velocity between t1 and t2.

D. the velocity at t1.

(1)

55. A particle is projected horizontally with speed v from a height H. It lands a horizontal distance R

from the point of launch as shown in the diagram below. v

H

R

A second particle is projected horizontally from the same height with speed 2v. Neglecting air resistance the horizontal distance travelled by this particle is

A. R.

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56. A small steel ball falls from rest through a distance of 3 m. When calculating the time of fall, air resistance can be ignored because

A. air is less dense than steel.

B. air resistance increases with the speed of the ball.

C. the air is not moving.

D. air resistance is much less than the weight of the ball.

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57. The graph shows the variation with time t of the velocity v of an object moving along a straight line.

v

0

t 0

Which graph shows the variation with time t of the acceleration a of the object?

a

0

t 0

a

0

t 0

a

0

t 0

a

0

t 0

A . B .

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58. Two identical metal spheres are held above the ground as shown.

s p h e r e s

( n o t t o s c a l e )

g r o u n d

The separation between them is small compared to their distance above the ground. When the spheres are released, the separation of the spheres will

A. remain constant.

B. decrease continuously.

C. increase continuously.

D. increase initially and then remain constant.

(1)

59. An object is falling, in air, towards the Earth’s surface.

What changes occur in the acceleration and in the velocity of the object as it approaches terminal velocity?

acceleration velocity

A. decreases to zero increases continuously

B. decreases to zero increases to a constant value

C. constant increases to a constant value

D. constant increases continuously

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60. A stone is thrown from the top of a cliff with speed v at an angle θ above the horizontal, as shown.

c l i f f

Air resistance is negligible and the acceleration of free fall is g.

What is the horizontal velocity of the stone a time t after the stone has been thrown? A. v sinθ

B. v sinθ – gt C. v cosθ D. v cosθ – gt

(1)

61. A car has a speed of + 15 m s–1 relative to the ground. It passes a cyclist travelling in the same

straight-line. The speed of the car relative to the cyclist is + 12 m s–1.

The speed of the cyclist relative to the ground is

A. –3.0 m s–1.

B. –1.5 m s–1.

C. +1.5 m s–1.

D. +3.0 m s–1.

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62. A steel sphere is dropped from rest in oil. Which of the following graphs best represents the variation with time of the speed of the sphere?

A . s p e e d

0

B . s p e e d

0

0 t i m e 0 t i m e

C . s p e e d

0

D . s p e e d

0

0 t i m e 0 t i m e

(1)

63. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to

t = T.

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64. The diagram below shows the trajectory of a ball thrown into the air. There is no air resistance. t r a j e c t o r y o f b a l l

X

A B

C D

Which arrow gives the direction of the resultant force on the ball at the point X?

A. A

B. B

C. C

D. D

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65. A ball is thrown vertically upwards from the ground. The graph shows the variation with time t of the vertical displacement d of the ball.

Which of the following gives the final displacement after time T and the average speed between time t = 0 m aand time t = T?

Displacement Average speed

A. 0 0

B. 0

T D

2

C. 2D

T D

2

D. 2D 0

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66. The graph below shows the variation with time t of the velocity v of an object moving on a straight-line.

Which of the graphs below best represents the variation with time t of the acceleration a of the object?

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