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Kinematics – Paper 1
1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T.
a
00 T t
The shaded area under the graph represents change in
A. displacement.
B. velocity.
C. momentum.
D. kinetic energy.
2. The graph below shows the variation with time t of the acceleration a of a body moving in a straight-line.
a
00 t t t1 2
The shaded area represents
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.
2
3. The diagram below shows the variation with time t of the velocity v of an object.
v
t00
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.
4. The graph below shows the variation with time t of the acceleration a of a spaceship.
a
00 T 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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5. The graph below shows the variation with time t of the acceleration a of a spaceship.
a
00 T 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.
6. 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. speed
0
B. speed
00 time 0 time
C. speed
0
D. speed
00 time 0 time
4
7. The diagram below shows the variation with time t of the velocity v of an object.
v
t00
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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8. 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.
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9. 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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10. 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
8
11. 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.
(1)
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12. 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. velocity
0
B. velocity
0 0 time
0 time
C. velocity
0
D. velocity
00 time 0 time
13. 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
00 tA B C D
10
14. The graph shows the variation with time t of the velocity v of an object moving along a straight line.
v
0 t0
Which graph shows the variation with time t of the acceleration a of the object?
a
0t0
a
0t0
a
0t0
a
0t0
A. B.
C. D.
11
15. 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
12
16. 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
TT
T
tt
t
v
vv
v
0
00
00
000
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17. 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?
14
18. 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.
speed
speed
speed
speed
T
T
T
T
t
t
t
t
0
0
0
0
0
0
0
0
A. B.
C. D.
VHVH
VH VH
VV VV
VVVV
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19. 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
20. 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.
16
21. 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
22. The diagram below shows the path of a projectile in the absence of air resistance.
Verticalposition
Horizontal position
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.)
Verticalposition
Verticalposition
Verticalposition
Verticalposition
Horizontal position Horizontal position
Horizontal position Horizontal position
A. B.
C. D.
17
23. 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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24. 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
PQ
Q
Q
Q
S
S S
S
A. B.
C. D.
19
25. 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.
20
26. 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
EW
Bird10 m s
4 m s
Car–1
–1
Which one of the following vectors represents the velocity of the bird relative to a person in the car?
A.
C.
B.
D.
(1)
27. 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.
B. .2R
C. 2R.
D. 4R.
21
28. The graph shows the variation with time t of the acceleration a of an object.
0
20
15
10
5
a / ms –2
0 1 2 3 4 5 6 7 8 9 10t / 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.
22
29. Peter and Susan both stand on the edge of a vertical cliff.
Sea
V (Peter)
V (Susan)
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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30. 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.
31. 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.
Building
X Y
v
v
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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32. 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
33. The minute hand of a clock hung on a vertical wall has length L.
LP
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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34. 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
35. 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
A. T
P and Q ofnt displaceme
TP toQ from speedin change
B. T
P and Q ofnt displaceme
TP toQ fromy in velocit change
C. T
P and Qbetween distance
TP toQ from speedin change
D. T
P and Qbetween distance
TP toQ fromy in velocit change
36. 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.
26
37. Points P and Q are at distances R and 2R respectively from the centre X of a disc, as shown below.
Q
P 2R
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
27
38. A stone is thrown with speed v from the top of a cliff of height H, as shown below.
h v
cliff
H
sea
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. ( )ghv 2+
B. ( )gHv 2+
C. { }( )Hhg +2
D. ( )gHv 22 +
28
39. A stone is thrown from the top of a cliff with speed v at an angle θ above the horizontal, as shown.
cliff
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
29
40. The diagram below shows the trajectory of a ball thrown into the air. There is no air resistance.
trajectory of ballX
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
30
41. 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.
initial position
d
v
The speed of the body when it has travelled a distance 2d
from its initial position is
A. .4v
B. .2v
C. .2v
D. .22v
31
42. 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
table
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
43. Which of the following is a correct definition of average acceleration?
A. takentime
yin velocit change
B. takentime
velocity
C. takentime
speedin change
D. takentime
speed
32
44. 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.
ground
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.
45. 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
33
46. 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.
47. Two identical metal spheres are held above the ground as shown.
spheres
(not to scale)
ground
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.
34
48. 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
49. 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
Answers
1. B
2. A
3. B
4. B
5. B
6. A
7. D
8. A
9. A
10. D
11. A
35
12. C
13. A
14. A
15. C
16. C
17. A
18. B
19. B
20. C
21. B
22. A
23. A
24. A
25. C
26. B
27. C
28. C
29. B
30. A
31. C
32. B
33. A
34. C
35. B
36. D
37. C
38. D
39. C
40. D
41. C
42. A
36
43. A
44. C
45. C
46. D
47. A
48. D 49. D
