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CAIE A-Level Physics AS 2.1 Equations of Motion Questions

Practise selecting kinematics definitions, graphs and equations for motion, free fall, projectiles and experiments, checking uncertainty and feasibility.

Syllabus
2028–2030
Course
Physics 9702
Level
AS

Exam points

  • Represent motion with distance, displacement, speed, velocity and acceleration graphs, reading gradients, areas, signs and turning features.
  • Determine displacement from velocity–time area and velocity/acceleration from displacement–time or velocity–time gradients.
  • Derive and apply uniformly accelerated-motion equations, including sign conventions and vertical free fall.
  • Describe the free-fall experiment and control timing, distance, uncertainty and safety.
  • Resolve perpendicular uniform-velocity and uniform-acceleration components to analyse projectile-style paths.

Covered syllabus points

2.1.1—Distance, displacement, speed, velocity and acceleration2.1.2—Distance, displacement, speed, velocity and acceleration2.1.3—Displacement from the area under a velocity–time graph2.1.4—Velocity using the gradient of a displacement–time graph2.1.5—Acceleration using the gradient of a velocity–time graph2.1.6—Derive, from the definitions of velocity and acceleration, equations that2.1.7—Equations that represent uniformly accelerated motion in a straight line2.1.8—The acceleration of free fall using a falling object2.1.9—Motion due to a uniform velocity in one direction and a uniform acceleration

Question 1

[Maximum number: 1]

A pendulum consists of a solid sphere suspended by a string from a fixed point P , as shown in Fig. 3.1.

Fig. 3.1 (not to scale)

Fig. 3.1 (not to scale)

The sphere swings from side to side. At one instant the sphere is at its lowest position X , where it has kinetic energy 0.86 J and momentum 0.72 Ns in a horizontal direction. A short time later the sphere is at position Y , where it is momentarily stationary at a maximum vertical height h above position X.

The string has a fixed length and negligible weight. Air resistance is also negligible.

On Fig. 3.1, draw a solid line to represent the displacement of the centre of the sphere at position Y from position X .

Question 2

[Maximum number: 5]

A child on a sledge slides down a steep hill and then travels in a straight line up an ice-covered slope, as illustrated in Fig. 3.1.

Fig. 3.1 (not to scale)

Fig. 3.1 (not to scale)

The sledge passes point A with speed 18 ms−118 \mathrm{~ms}^{-1} at time t=0 and then comes to rest at point B. The child applies a brake to the sledge at point B. The brake does not keep the sledge stationary and it immediately slides back down the slope towards A .

The variation with time t of the velocity v of the sledge from t=0 to t=24 st=24 \mathrm{~s} is shown in Fig. 3.2.

Fig. 3.2

Fig. 3.2

Question (a)

(a)

State the time taken for the sledge to travel from A to B .
time =

[ 1 ]

Question (b)

(b)

Determine the displacement of the sledge up the slope from point A at time t=24 st=24 \mathrm{~s}.

displacement =
[ 2 ]

Question (c)

(c)

Show that the acceleration of the sledge as it moves from B back towards A is 0.50 m s−20.50 \mathrm{~m} \mathrm{~s}^{-2}.

[ 2 ]

Question 3

[Maximum number: 4]

Question (a)

(a)

The string is now used to move the cylinder in (a) vertically upwards through the water. The variation with time t of the velocity v of the cylinder is shown in Fig. 2.2.

Fig. 2.2

Fig. 2.2

[ 4 ]

Question (i)

(i)

Use Fig. 2.2 to determine the acceleration of the cylinder at time t=2.0 st=2.0 \mathrm{~s}.
acceleration = ms−2\mathrm{ms}^{-2}

[ 2 ]

Question (ii)

(ii)

The top face of the cylinder is at a depth of 0.32 m below the surface of the water at time t=0.

Use Fig. 2.2 to determine the depth of the top face below the surface of the water at time t=4.0 st=4.0 \mathrm{~s}.
depth = m

[ 2 ]
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