A LevelMathsOCRMaths AMechanicsExam QuestionsKinematicsConstant Acceleration in 1D

Constant Acceleration in 1D (OCR A Level Maths A: Mechanics): Exam Questions

Exam code: H240

2 hours33 questions
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12 marks

The motion of a particle is modelled as having constant acceleration a space straight m space straight s to the power of negative 2 end exponent and initial velocity u space straight m space straight s to the power of negative 1 end exponent.

Use integration to show that its velocity, v space straight m space straight s to the power of negative 1 end exponent, at time t seconds, can be given by the equation  v space equals space u space plus space a t.

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2
Sme Calculator2 marks

A particle moves in a straight line.

Initially the particle is at rest.

After 4.5 seconds its speed is 10.35 ms-1.

Assuming the acceleration is constant throughout its motion, calculate the magnitude of the particle's acceleration.

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3
Sme Calculator2 marks

A particle travels 30 m in 8 seconds with constant acceleration 0.8 space straight m space straight s to the power of negative 2 end exponent.

Find the velocity of the particle at the end of this motion.

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4
Sme Calculator2 marks

A ball is dropped from rest from the top of a tall building.

Find the time taken for the velocity of the ball to reach 58.8 space ms to the power of negative 1 end exponent.

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5
Sme Calculator2 marks

A particle accelerates from rest to a velocity of 7.75 space ms to the power of negative 1 end exponent in 3.2 seconds.

Find the displacement of the particle from its starting point after 3.2 seconds.

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6
Sme Calculator2 marks

A ball is projected vertically upwards from the top of a tall building.

Six seconds later the ball is 124.38 space straight m below its initial position.

Find the velocity with which the ball was projected.

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72 marks

The motion of a particle is modelled as having constant acceleration a space straight m space straight s to the power of negative 2 end exponent, initial velocity u space straight m space straight s to the power of negative 1 end exponent and final velocity v space straight m space straight s to the power of negative 1 end exponent such that at time t seconds

v equals u plus a t

Use integration to show that the displacement, s m, of the particle from its initial position is given by

s equals u t plus 1 half space a t squared

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8
Sme Calculator2 marks

A particle passes a fixed point, O, with velocity 7.3 space ms to the power of negative 1 end exponent.

The particle then decelerates at a constant rate of 0.32 space straight m space straight s to the power of negative 2 end exponent.

Calculate the velocity of the particle when its displacement from O is 23 m.

Give your answer to three significant figures.

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9
Sme Calculator2 marks

A particle P moves in a straight line with constant acceleration.

During the first 60 seconds of its motion it travels 1932 metres, and after one minute its speed is 42.7 space ms to the power of negative 1 end exponent.

Calculate the magnitude of the constant acceleration of P.

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10
Sme Calculator2 marks

A particle passes a fixed point O at time t equals 0, with velocity 5.3 space ms to the power of negative 1 end exponent and immediately starts to decelerate at a constant rate of space 2 space ms to the power of negative 2 end exponent.

Determine the distance of the particle from the point O when t equals 7.6 space seconds.

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11
Sme Calculator2 marks

A particle P moves in a straight line with constant acceleration.

In the first 8.2 seconds of its motion it travels 30.75 m, and reaches a speed of 7.5 space ms to the power of negative 1 end exponent.

Show that the initial speed of P was 0 space ms to the power of negative 1 end exponent.

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12
Sme Calculator2 marks

A particle is projected upwards from ground level.

After 2.4 seconds, the particle is 8.5 m above the ground.

Find the velocity with which the particle was projected upwards.

Give your answer to three significant figures.

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13
Sme Calculator3 marks

A particle is travelling with constant acceleration 1.54 space straight m space straight s to the power of negative 2 end exponent.

Find the first time at which the particle is moving with velocity 13.8 space straight m space straight s to the power of negative 1 end exponent at a displacement of 61.8 space straight m from its starting point.

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14a
Sme Calculator2 marks

The motion of a particle is described by the velocity-time graph in Figure 1.

Graph showing velocity over time. Velocity increases from 2 to 20 units in 6 units of time, holds, then decreases back to 2 units by time T+10.

Work out the acceleration for the first 6 seconds of the particle’s motion.

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14b
Sme Calculator2 marks

Work out the distance covered by the particle in the last 10 seconds of its motion.

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14c
Sme Calculator2 marks

The particle travels a distance of 280 m whilst it has zero acceleration.

Find the value of T.

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1a
Sme Calculator2 marks

A car is being tested for safety by using a computer‑controlled car that is accelerated along a horizontal track and crashed into a wall.

The horizontal track is 750 m long, and the wall is at the end of the track.

During a particular crash test, the car starts from rest and has a constant acceleration of 1.5 space ms to the power of negative 2 end exponent.

Find the maximum speed, in metres per second, that the car can reach along the track.

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1b
Sme Calculator4 marks

(i) Calculate the distance from the wall a car should be placed such that when starting from rest, it will crash into the wall with a speed of 27 space straight m space straight s to the power of negative 1 end exponent?

(ii) In this case, calculate the length of time it will take for the car to reach the wall.

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2
Sme Calculator4 marks

A ball is projected vertically upwards from the ground with a velocity of 5.8 space ms to the power of negative 1 end exponent.

Find

(i) the maximum height the ball reaches above the ground,

(ii) and the time taken to reach the maximum height.

How did you do?

3a
Sme Calculator2 marks

Train A leaves a station, starting from rest, with constant acceleration. After 85 seconds it is passed by train B.

Train B left the same station, also starting from rest, 35 seconds after train A.

Train B moves with constant acceleration 1.4 space ms to the power of negative 2 end exponent throughout its motion.

Train B passes train A at point X.

Calculate the distance between the station and point X.

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3b
Sme Calculator2 marks

Calculate the acceleration of train A, giving your answer to three significant figures.

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4
Sme Calculator4 marks

A particle is projected vertically upwards from ground level with a velocity of 35.6 space ms to the power of negative 1 end exponent.

Find the length of time for which the particle is at least 15 m above the ground.

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5
Sme Calculator7 marks

A train leaves station O from rest with constant acceleration 0.12 space ms to the power of negative 2 end exponent.

190 seconds later it passes a signal at which point the train decelerates uniformly at space 0.18 space ms to the power of negative 2 end exponent until coming to rest at station X .

Find the distance between station O and station X.

How did you do?

6a
Sme Calculator4 marks

To crash test cars a computer‑controlled car is accelerated along a horizontal track and crashed into a wall. The maximum length of track available is 0.8 space km.

During a crash test, a car starts from rest and has constant acceleration.

In one test a car is driven at the wall with constant acceleration 1.6 space ms to the power of negative 2 end exponent.

Find the maximum speed, in kilometres per hour, with which it could hit the wall.

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6b
Sme Calculator3 marks

The standard setting for testing is a constant acceleration of 1.2 space ms to the power of negative 2 end exponent, but this can be varied up or down by 40% prior to a test being carried out.

Determine if it is possible to crash test a car at a speed of 200 space kmh to the power of negative 1 end exponent.

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72 marks

The diagram below shows the velocity-time graph for a particle having initial velocity space u space straight m space straight s to the power of negative 1 end exponent and velocity space v space straight m space straight s to the power of negative 1 end exponent at time t seconds.

Graph showing velocity on the vertical axis and time on the horizontal axis. A line slopes upward from initial velocity u to final velocity v at time t.

(i) Explain how the graph shows that the acceleration of the particle is constant.

(ii) Use the graph to show that the displacement of the particle, from its position at t space equals space 0, is given by

s space equals space 1 half t open parentheses u space plus space v close parentheses

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83 marks

Use the constant acceleration equations 

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

to show that

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

How did you do?

1
Sme Calculator4 marks

A ball is projected vertically upwards from ground level.

1.6 seconds after reaching its maximum height, the ball hits the ground.

Find

(i) the maximum height the ball reached,

(ii) the velocity with which it was projected.

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2
Sme Calculator4 marks

A car travelling along a horizontal road passes a point A with velocity 21 space ms to the power of negative 1 end exponent and constant acceleration 0.2 space ms to the power of negative 2 end exponent.

Point B is 1.5 space km from point A. When the car reaches point B it decelerates uniformly at 3.1 space ms to the power of negative 2 end exponent until it comes to rest.

Find the distance the car travels from the moment it starts to decelerate until it comes to rest.

How did you do?

3a
Sme Calculator6 marks

Train A leaves a station from rest with constant acceleration 0.12 space ms to the power of negative 2 end exponent.

After 40 seconds have elapsed, train B leaves the station from rest with constant acceleration 0.2 space ms to the power of negative 2 end exponent, travelling along the same track as train A.

Find the length of time from when train B leaves the station to when it catches up with train A.

Give your answer to three significant figures.

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3b
Sme Calculator2 marks

Find the distance, in kilometres, that both trains have travelled when train A catches up with train B. Give your answer to three significant figures.

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4a
Sme Calculator6 marks

A train leaves station O from rest with a constant acceleration of 0.2 space ms to the power of negative 2 end exponent.

After 125 space seconds it passes a signal at which point the train decelerates uniformly until coming to rest at station X, 75 seconds later.

Find the distance between station O and station X.

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4b
Sme Calculator4 marks

The train then leaves station X  but travels in the opposite direction with constant acceleration 0.1 space ms to the power of negative 2 end exponent.

The train does not stop at station O but 300 space seconds after leaving station X  it passes a sign indicating that station Y  is 850 m away. At this point the train starts to decelerate uniformly so that it comes to rest at station Y.

Find the distance between station O and station Y.

How did you do?

54 marks

A particle moves with constant acceleration, a space straight m space straight s to the power of negative 2 end exponent, such that its initial velocity is u space straight m space straight s to the power of negative 1 end exponent and t seconds later its velocity is v space straight m space straight s to the power of negative 1 end exponent.

Use calculus to show that the displacement of the particle, s m, from its initial position is given by

s space equals space v t space minus space 1 half a t squared

Show clear working for each stage of your solution.

How did you do?

6
Sme Calculator2 marks

A stone is projected vertically downwards from the top of a cliff with initial speed 0.3 space straight m space straight s to the power of negative 1 end exponent. The stone hits the sea below after 3.2 seconds.

Calculate the height of the cliff.

How did you do?

1
Sme Calculator8 marks

A car travels along a horizontal road and passes a point A with velocity 17.2 space ms to the power of negative 1 end exponent and constant acceleration 0.4 space ms to the power of negative 2 end exponent.

Point B is 0.8 space km from point A. When the car reaches point B it starts decelerating at a constant rate of 2.75 space straight m space straight s to the power of negative 2 end exponent until it comes to rest at point C.

Find the time taken by the car to travel from point A to point C.

Give your answer to one decimal place.

How did you do?

2
Sme Calculator5 marks

A train leaves station A from rest, heading in the direction of station B with a constant acceleration of magnitude 0.2 space ms to the power of negative 2 end exponent .

At the same time, another train leaves station B from rest, heading in the direction of station A with a constant acceleration of magnitude 0.16 space ms to the power of negative 2 end exponent.

The distance between station Aand station B is 8.2 space km.

Determine the distance from station A to the point at which the two trains meet.

Give your answer in kilometres to 2 decimal places.

How did you do?

3a
Sme Calculator3 marks

Figure 1 shows a velocity time graph for the motion of two particles.

The motion of particle A is shown by the solid line, and the motion of particle B is shown by the dotted line.

Graphs intersect at (T1, 5) and t=T2. The dashed line increases from 0 to 8 in 15 seconds, and decreases to (0, 25). Where T2 is located, the dashed line is going downwards and the solid line is increasing from (12, 5) to (21, 10)

Find the value of T subscript 1, giving your answer to three significant figures.

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3b
Sme Calculator9 marks

Find the value of T subscript 2, giving your answer to three significant figures.

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4
Sme Calculator7 marks

Two trains leave station O, both from rest at the same time, in opposite directions.

The first train travels with constant acceleration of magnitude 0.15 space straight m space straight s to the power of negative 2 end exponent.

The second train travels with constant acceleration of magnitude 0.24 space straight m space straight s to the power of negative 2 end exponent until it reaches a signal 210 seconds later. At this point it starts to decelerate uniformly until coming to rest at station X, 60 seconds later.

After a 2-minute wait at station X, the second train leaves in the opposite direction (back towards O) with constant acceleration of magnitude 0.8 space straight m space straight s to the power of negative 2 end exponent.

Find the distance between the two trains 10 minutes after they both left station O.

How did you do?

5a
Sme Calculator7 marks

A ball is projected vertically upwards from ground level with speed 29.3 space straight m space straight s to the power of negative 1 end exponent.

At the same time, a second ball is projected vertically downwards from a height of 150 m above ground level, directly above the first ball, with speed 8.2 space straight m space straight s to the power of negative 1 end exponent.

Find

(i) the time it takes the two balls to collide,

(ii) the height above the ground at which this collision occurs.

How did you do?

5b
Sme Calculator6 marks

Find the speed of each ball at the point when they collide, and state their direction of motion when the collision occurs.

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