CIE A Level Physics

Topic Questions

A LevelPhysicsCIETopic Questions2. Kinematics2.1 Equations of Motion

Syllabus Edition

First teaching 2020

Last exams 2024

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2.1 Equations of Motion

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1a
Sme Calculator4 marks

State the difference between

(i)
distance and displacement,
[2] 
(ii)
speed and velocity.
[2]

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1b
Sme Calculator6 marks

Complete the table in Table 1.1 to describe the features of displacement-time, velocity-time and acceleration-time graphs represent.

 Place a cross (✘) in any grid space which does not represent anything. Some grid spaces have been completed for you.

 

Table 1.1

  displacement-time velocity-time acceleration-time
gradient represents     ✘
area under curve represents      
y-intercept represents      
horizontal line represents zero velocity    
straight section represents      
curved section represents   non-uniform acceleration  

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1c
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On Fig. 1.2, sketch the variation of time with displacement, velocity, and acceleration for an object moving with constant velocity.

Take the initial displacement as zero. 

2-1-1c-e-2-1-motion-graphs-blank-cie-ial-sq

Fig. 1.2

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1d
Sme Calculator3 marks

On Fig. 1.3, sketch the variation of time with displacement, velocity, and acceleration for an object moving with uniform acceleration. 

Take the initial displacement as equal to zero.

 

2-1-1c-e-2-1-motion-graphs-blank-cie-ial-sq

Fig. 1.3

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2a
Sme Calculator2 marks

Place ticks (✓) in the table in Table 1.1 to indicate which of the quantities are vectors and which are scalars.

 

Table 1.1

  velocity speed distance displacement acceleration
vector          
scalar          

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2b
Sme Calculator3 marks

Two of the equations of uniformly accelerated motion are

s space equals space u t space plus space 1 half a t squared

v squared space equals space u squared space plus space 2 a s

State

 
(i)
the definition of uniform acceleration,
[1]
(ii)
the two other equations of motion that can be used to derive the above equations.
[2]

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2c
Sme Calculator5 marks

Fig. 1.2 shows an electric motor which is used to lift and lower heavy loads.

2-1-2c-e-2-1-pulley-load-kinematics-cie-ial-sq

Fig. 1.2

Initially, the load is on the ground. Fig. 1.3 shows the variation of the displacement s of the load with time t.

2-1-2c-e-2-1-displacement-time-graph-pulley-load-cie-ial-sq

Fig. 1.3

(i)
Complete Table 1.4 to show the magnitude and direction of the velocity of the load during the time intervals shown.
 

Table 1.4

time interval magnitude of velocity direction of velocity
t = 0 to 2.0 s    
t = 2.0 to 3.5 s    
t = 3.5 to 4.0 s    
[3]
 
(ii)
On Fig. 1.5, sketch a graph to show the variation of the velocity v of the load with time t.
 
Include values for velocity on the v-axis.
[2]

2-1-2c-e-2-1-velocity-time-graph-blank-cie-ial-sq

Fig. 1.5

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2d
Sme Calculator2 marks

As the load is lowered towards the ground, the string breaks when t = 4.0 s. It then falls vertically toward the ground.

Calculate the velocity of the load just before it hits the ground.

Assume air resistance is negligible.

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3a
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A student drops a stone into a well and measures the time it takes to hear the stone splash at the bottom.

Explain how this measurement of time can be used to find the depth of the well.

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3b
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It takes 3.2 s for the stone to drop from rest and splash into the water at the bottom.
 

Calculate the speed of the stone when it hits the water.

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3c
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On Fig. 1.1, sketch the variation of time with velocity for the stone as it falls down the well.

 

2-1-3c-e-2-1-free-fall-motion-graph-blank-cie-ial-sq

Fig. 1.1

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3d
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Use your graph from (c) to determine the depth of the well.

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1a
Sme Calculator5 marks

During a fireworks display, a firework is launched into the air and explodes once it reaches a maximum height of 250 m.

The vertical component of the velocity at launch depends on both the initial velocity of the firework and the angle θ between the initial velocity and the horizontal.

The maximum initial velocity a firework can be launched at is 110 m s−1.

(i)
Calculate the initial launch velocity for a firework that is fired directly upwards.
[2]
 
(ii)
Show that the minimum launch angle between the initial velocity and the horizontal to reach 250 m is about 40°.
[3]

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1b
Sme Calculator4 marks

On Fig. 1.1, sketch the variation of angle θ with the initial velocity required for the firework to reach the maximum height of 250 m. 

Include values from (a) on the axes.

 

2-1-1b-h-2-1-h-projectile-motion-fireworks-cie-ial-sq

Fig. 1.1

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1c
Sme Calculator4 marks

The length of the fuse within the firework is chosen to ensure it explodes just as it reaches its highest point above the ground.

The firework is launched into the air at an angle of 75° to the horizontal, as shown in Fig. 1.2.

2-1-1c-h-2-1-h-projectile-motion-fireworks-fuse-length-cie-ial-sq

Fig. 1.2

The firework contains a fuse with a burn rate of 1.5 cm s–1.

Determine the length of the fuse used in the firework.

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1d
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During the display, one of the fireworks is lit but falls over before launching. When it launches, it leaves the ground with an initial velocity of 75 m s−1 at an angle of 30° to the horizontal, as shown in Fig. 1.3.

The firework moves in the direction of a hill. The side of the hill is inclined at 8.5° to the horizontal, as shown.

2-1-1d-h-2-1-h-projectile-motion-fireworks-hillside-cie-ial-sq

Fig. 1.3

Deduce whether the firework ignites before it lands on the hillside.

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2a
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Fig. 1.1 shows a stunt motorcyclist descending down a ramp.

2-1-2a-h-2-1-h-motorcyclist-projectile-ramp-cie-ial-sq

Fig. 1.1

The motorcyclist starts from rest at the top of the ramp at A and leaves the ramp at B horizontally.

After leaving the ramp at B, the motorcyclist lands on the ground at C, which is 6.4 m away. At C, the motorcyclist lands with a resultant velocity of 13.4 m s–1 at an angle of 29.5° with the horizontal.

Calculate the initial velocity of the motorcyclist at B. 

In this question, assume that air resistance is negligible.

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2b
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The motorcyclist practices a stunt on a different ramp inclined at 25º and 3 m high as shown in Fig. 1.2.

The other ramp is 24 m away and has a height of 1 m, as shown.

2-1-2b-h-2-1-h-motorcyclist-projectile-two-ramps-cie-ial-sq

Fig. 1.2

Calculate the minimum initial velocity the motorcyclist requires in order to reach the other ramp.

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2c
Sme Calculator4 marks

The stunt motorcyclist's ultimate goal is to jump across a river and land on the other side. Fig. 1.3 shows the motorcyclist driving off a ramp at the edge of a river.

2-1-2c-h-2-1-h-motorcyclist-projectile-river-jump-cie-ial-sq

Fig. 1.3

 

The ramp is at an angle of 25° to the horizontal and the height at the end of the ramp is 3.0 m. The width of the river is 100 m. The initial velocity of the motorcyclist is 35 m s−1.

Deduce whether the motorcyclist lands on the other side of the river.

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2d
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Explain how air resistance would affect the jump.

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3a
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An object is released near the surface of the Moon at time t = 0. Fig. 1.1 shows the variation of displacement s with time t of the object from the point of release. 

sl-sq-2-1-hard-q3a

Fig. 1.1

(i)
State the significance of the negative values of s.
[1]
 
(ii)
State two assumptions about the motion of the object. 
[2]

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3b
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Use the graph in Fig. 1.1 to determine a value for the acceleration of free fall close to the surface of the Moon.

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3c
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Use Fig. 1.1 to estimate the instantaneous velocity of the object when t = 1.5 s.

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3d
Sme Calculator4 marks
(i)
On Fig. 1.1, sketch the variation of displacement s with time t if the same object was released close to the surface of the Earth instead.
[2]
 
(ii)
Describe and explain the features of your sketch. 
[2]

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1a
Sme Calculator1 mark

Define acceleration.

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1b
Sme Calculator7 marks

A ball is kicked from horizontal ground towards a vertical wall, as shown in Fig. 1.1.

q2b-paper-2-specimen-2022-cie-ial-physics

Fig. 1.1 (not to scale)

The horizontal distance between the initial position of the ball and the base of the wall is 24 m. The ball is kicked with an initial velocity v at an angle of 28° to the horizontal. The ball hits the top of the wall after a time of 1.5 s. Air resistance is negligible.

(i)
Calculate the initial horizontal component vx of the velocity of the ball.


vx = ................................................. m s–1 [1]

(ii)
Show that the initial vertical component vy of the velocity of the ball is 8.5 m s–1.

[2]

(iii)
Calculate the time taken for the ball to reach its maximum height above the ground.



time = ....................................................... s [2]

(iv)
The ball is kicked at time t = 0. Assume that the vertical component vy of the velocity of the ball is positive in the upwards direction.
 
On Fig. 1.2, sketch the variation with time t of vy for the time until the ball hits the wall.
 

q2b-iv-paper-2-specimen-2022-cie-ial-physics

Fig. 1.2

[2]

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1c
Sme Calculator4 marks
(i)
Calculate the maximum height above the ground of the ball in (b).



maximum height = ...................................................... m  [2]

(ii)
The maximum gravitational potential energy of the ball above the ground is 22 J.

Calculate the mass of the ball.



mass = ..................................................... kg  [2]

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1d
Sme Calculator1 mark

A ball of greater mass is kicked with the same velocity as the ball in (b).

Air resistance is still negligible. 

State and explain the effect, if any, of the increased mass on the time taken by the ball to reach its maximum height.

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2a
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A boy standing on a cliff shoots a pellet from his pellet gun vertically upwards. The variation of displacement s of the pellet with time t is shown in Fig. 1.1.

2-1-2a-m-2-1-motion-graph-stone-vertical-throw-displacement-cie-ial

(i)
Determine the initial speed of the pellet, at t = 0 s.
[3]
(ii)
Determine the speed of the pellet at t = 6.0 s.

[2]

(iii)
State an assumption made in these calculations.
[1]

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2b
Sme Calculator3 marks

On Fig. 1.2, sketch the variation of velocity v of the pellet with time t.

Include your values from (a) on the axes.

 

2-1-2b-m-2-1-motion-graph-stone-vertical-throw-velocitycie-ial

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2c
Sme Calculator4 marks

Using Fig. 1.2

 
(i)
Determine the maximum height reached by the pellet.
[2]
(ii)
Show that the final displacement of the pellet after 6.0 s is about 30 m below the starting point.
[2]

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2d
Sme Calculator5 marks

An identical pellet gun is fired horizontally off the edge of the cliff at the exact same time the other gun is fired vertically upwards. The vertically fired pellet is in motion for exactly 6.0 s before hitting the ground below the edge of the cliff.

Both pellets have the same initial speed.

(i)
State which pellet hits the ground first. 
[1]
(ii)
Calculate the time difference between the pellets hitting the ground.
[4]

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3a
Sme Calculator4 marks

A ball is projected horizontally at 27 m s–1 from a vertical cliff. It travels a horizontal distance of 40 m before hitting the ground.

Assume that air resistance is negligible.q1a_motion_sl-ib-physics-sq-medium

Calculate the vertical velocity of the ball just before it hits the ground.

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3b
Sme Calculator2 marks

Calculate the height of the cliff.

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3c
Sme Calculator3 marks

Sketch the graphs to show how the horizontal and vertical components of the velocity of the ball, v subscript x and v subscript y change with time t just before the ball hits the ground.

Label any appropriate values on the axes.

q1c_motion_sl-ib-physics-sq-medium

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3d
Sme Calculator2 marks

Calculate the resultant velocity of the ball just before it hits the ground.

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4a
Sme Calculator8 marks

A particle moves in a straight line with a constant acceleration, a. The initial velocity of the particle at t = 0 is u.  After a further time t, its velocity has increased to v.

 
(i)
Using the definition of acceleration, show that 
 
v space equals space u space plus space a t
[2]
(ii)
Using the definition of average velocity, show that 
 
s space equals space u t space plus space 1 half a t squared
[3]
(iii)
Using these two equations, show that 
 
v squared space equals space u squared space plus space 2 a s
[3]

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4b
Sme Calculator4 marks

A student investigates the motion of a light ball bearing as it falls from rest alongside a vertical 100 cm scale.

The student sets up a camera to take flash photographs of the ball at 0.05 s intervals, as shown in Fig. 1.1.

2-1-4b-m-2-1-vertical-drop-100cm-scale-cie-ial

The first photograph is taken at time t = 0.

Using Fig. 1.1, describe and explain the motion of the ball

 
(i)
in the interval t = 0 to t = 0.3 s
[2]
(ii)
in the interval t = 0.35 to t = 0.55 s.
[2]

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4c
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The 100 cm scale is suspended 160 cm above the ground.

Determine the total time that the ball spends in free fall after it is dropped from the starting point of the 100 cm scale.

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4d
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The student repeats the experiment with a lead sphere that falls with constant acceleration and does not reach a constant speed.

Determine the number of photographs, including the photograph at t = 0, that will be observed against the 100 cm scale.

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5a
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An archer fires an arrow towards a target as shown in Fig. 1.1.

2-1-5a-m-2-1-projectile-arrow-launch-cie-ial-sq

The centre of the target is at the same height as the initial position of the arrow.

The target is a distance of 100 m from the arrow. The arrow has an initial velocity of 62 m s–1 and is fired at an angle of 11° to the horizontal.

Describe how the vertical and horizontal components of the arrow's velocity change from when it is fired until it reaches its maximum height. 

Assume that the effect of air resistance is negligible.

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5b
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Show that the time taken for the arrow to reach its maximum height is about 1.2 s.

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5c
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Calculate the horizontal distance, measured along the base line, by which the arrow misses the target.

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