AQA AS Maths: Mechanics

Topic Questions

2.3 Constant Acceleration - 1D

1
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3 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. 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
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3 marks

Initially at rest, 4.5 seconds later a particle has velocity 10.35 space straight m space straight s to the power of negative 1 end exponent.

Given that it is constant throughout this motion, find the acceleration of the particle.

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3
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3 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
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3 marks

A ball is dropped from rest from the top of a tall building. How long does it take for the velocity of the ball to reach 58.8 space straight m space straight s to the power of negative 1 end exponent ?

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5
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3 marks

A particle moves from rest to velocity 7.75 space straight m space straight s to the power of negative 1 end exponent in 3.2 seconds. Find the displacement of the particle.

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6
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3 marks

A ball is projected upwards from the top of a tall building. 6 seconds later the ball is 124.38 space straight m below its initial position. Find the velocity with which the ball is projected.

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7
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3 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

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
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3 marks

A particle passes a fixed point, O, with velocity 7.3 space straight m space straight s to the power of negative 1 end exponent and then decelerates at a constant 0.32 space straight m space straight s to the power of negative 2 end exponent. Find the velocity of the particle when its displacement from O is 23 m. Give your answer to three singificiant figures.

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9
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3 marks

In one minute, a particle travels a distance of 1932 m. At this point, its velocity is 42.7 space straight m space straight s to the power of negative 1 end exponent.  Assuming it is constant, find the acceleration of the particle.

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10
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3 marks

A particle passes a fixed point, O, with velocity 5.3 space straight m space straight s to the power of negative 1 end exponent and then decelerates at a constant space 2 space straight m space straight s to the power of negative 2 end exponent.Determine the distance of the particle from O 7.6 space seconds later.

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11
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3 marks

A particle travels 30.75 m in 8.2 seconds, at which point it has velocity space 7.5 space straight m space straight s to the power of negative 1 end exponent. Show that the particle was initially at rest.

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12
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3 marks

A person holding a stone drops it from the top of a cliff. Assuming it has not reached the sea below find the distance travelled by the stone at the point when its velocity is 18.8 space straight m space straight s to the power of negative 1 end exponent. Give your answer to three significant figures.

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13
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3 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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14
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4 marks

A particle is travelling with constant acceleration 1.54 space straight m space straight s to the power of negative 2 end exponent. After it has travelled 61.8 space straight m the particle has velocity 13.8 space straight m space straight s to the power of negative 1 end exponent . Find the time it takes the particle to travel this far.

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1
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4 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

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2
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4 marks

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

Find how long the particle remains at least 15 m above the ground for.

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3
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5 marks

A car travelling along a horizontal road passes a point A with velocity 21 space straight m space straight s to the power of negative 1 end exponent and constant acceleration 0.2 space straight m space straight s to the power of negative 2 end exponent. Point B is 1.5 km from point A. When the car reaches point B it decelerates uniformly at 3.1 space straight m space straight s 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. Give your answer to an appropriate degree of accuracy.

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4a
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5 marks

A train leaves a station from rest with constant acceleration 0.12 space straight m space straight s to the power of negative 2 end exponent. 40 space seconds later another train leaves the station from rest with constant acceleration 0.2 space straight m space straight s to the power of negative 2 end exponent, travelling along the same track as the first train.

Find how long it will take the second train to catch up with the first.

Give your answer to three significant figures.

4b
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2 marks

How far, in kilometres, would both trains have travelled when the second one catches up with the first?
Give your answer to three significant figures.

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5
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6 marks

The motion of a particle is described by the velocity-time graph below.

picture4

The distance the particle travels from t space equals space T spacetot space equals space 36 is 150 m.

The distance the particle travels for the whole motion is 309 m.

Find the values of T and V.

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6
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5 marks

A ball is projected upwards from ground level. 1.6 seconds after reaching its maximum height the ball hits the ground. Find the maximum height the ball reaches and the velocity with which it was projected. Give your answers to an appropriate degree of accuracy.

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7a
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5 marks

A train leaves station O, from rest with constant acceleration 0.2 space straight m space straight s to the power of negative 2 end exponent. 125 space seconds later 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.

7b
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3 marks

The train then leaves station X  but travels in the opposite direction with constant acceleration 0.1 space straight m space straight s to the power of negative 2 end exponent. The train does not stop at station O but 300 space seconds after leaving station it passes a signal indicating that station Y  is 850 m away. At this point the train decelerates uniformly so it comes to rest at station Y.

Find the distance between station O and station Y

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8a
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4 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 long.

During a crash test, a car starts from rest and has constant acceleration. This is set to 1.2 space straight m space straight s to the power of negative 2 end exponent but can be varied up or down by 40% prior to a test being carried out.

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

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

8b
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3 marks

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

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1
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3 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.

nauricul_picture2

(i)
Explain how the graph shows that the acceleration of the particle is constant.
(ii)
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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2a
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3 marks

A particle is projected upwards from ground level with velocity u space straight m space straight s to the power of negative 1 end exponent. 6 seconds later it has a velocity of 1.2 space straight m space straight s to the power of negative 1 end exponent. Find the value of u.

2b
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3 marks

Find the displacement of the particle, from its initial position, 4 seconds later.

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3
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4 marks

A car travelling along a horizontal road passes a point A with velocity 21 space straight m space straight s to the power of negative 1 end exponent and immediately decelerates at a constant rate. The car comes to rest 260 m beyond point A. Find the magnitude of the deceleration of the car, giving your answer to three significant figures.

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4a
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3 marks

 Train  leaves a station, starting from rest, with constant acceleration. After 85 seconds it is passed by train B, that had left the same station 35 seconds after train A, also from rest with constant acceleration 1.4 space straight m space straight s to the power of negative 2 end exponent.

(i)
How long after it leaves the station does train B pass train A?
(ii)
Find the distance covered by both trains when train B passes train A.
4b
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4 marks

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

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5a
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2 marks

The motion of a particle is described by the velocity-time graph below.

picture3

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

5b
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2 marks

Work out the displacement of the particle in the last 10 seconds of its motion?

5c
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3 marks

The particle travels a distance of 280 m whilst it has zero acceleration. How long does the particle have zero acceleration for? Hence find the value of T?

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6
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4 marks

A ball is projected upwards from ground level with a velocity of 5.8 space straight m space straight s to the power of negative 1 end exponent. Find the maximum height the ball attains and the time it takes to reach it. Give your answers to an appropriate degree of accuracy.

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7
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5 marks

A train leaves station O, from rest with constant acceleration 0.12 space straight m space straight s 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 straight m space straight s to the power of negative 2 end exponent until coming to rest at station X .

Find the distance between station O and station X.

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8a
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3 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 750 m.

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

Find the maximum speed, in metres per second, that a car can be crash tested at.

8b
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4 marks
(i)
How far from the wall should a car be positioned such that it will crash with a speed of 27 space straight m space straight s to the power of negative 1 end exponent?
(ii)
How long will it take for the car to reach the wall?

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1
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4 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. 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

 

Clearly explain each stage of your solution.

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2
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6 marks

A car travelling along a horizontal road passes a point A with velocity 17.2 space straight m space straight s to the power of negative 1 end exponent and constant acceleration 0.4 m s-2. Point B is 0.8 km from point A. When the car reaches point B it starts decelerating at a constant 2.75 space straight m space straight s to the power of negative 2 end exponent. Find the time it takes the car to come to rest from point A. Give your answer to one decimal place.

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3
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6 marks

A train leaves station A, heading in the direction of station B, from rest with constant acceleration 0.2 space straight m space straight s to the power of negative 2 end exponent . At the same time, another train leaves station B, heading in the direction of station A, from rest with constant acceleration 0.16 space straight m space straight s to the power of negative 2 end exponent. The distance between the two stations is 8.2 space km. Modelling both trains as particles, find the distance they are from station A when they pass each other. Give your answer to the nearest 0.5 space km.

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4
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3 marks

 A stone is projected directly 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. Find the height of the cliff.

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5
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7 marks

The graph below shows the motion of two particles. Particle A’s motion is shown by the solid line, particle B’s motion is shown by the dotted line.

2-3-vh-q5--edexcel-al-mechanics

Find T1 and T2, giving your answers to three significant figures.

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6a
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4 marks

A firework is launched directly upwards from the top of a 135 m tall skyscraper with velocity 38.5 space straight m space straight s to the power of negative 1 end exponent.

Find the time for which the firework remains above 150 m from ground level.

6b
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3 marks

The firework explodes 2 seconds after reaching its maximum height. Find the height above the ground at which the firework explodes.

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7
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7 marks

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

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

The second train travels with constant acceleration 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 which point it decelerates 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 with constant acceleration 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.

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8a
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2 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 1.1 km long.

During a crash test, 20 space straight m of track is required to increase a car’s speed from rest to 5 space straight m space straight s to the power of negative 1 end exponent. From this point onwards a car is accelerated at a constant rate. This is set to space 2.1 space straight m space straight s to the power of negative 2 end exponent but can be varied up or down by 30% prior to a test being carried out.

 

Find the acceleration of a car during the first 20 m of a crash test.

8b
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3 marks

Determine if it is possible to crash test a car at a speed of 250 space km space straight h to the power of negative 1 end exponent.

8c
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5 marks

A crash test is unreliable if it takes under 10 seconds.
Find the lowest speed, in kilometres per hour, a car can be reliably crash tested at.

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9a
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6 marks

A ball is projected directly 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 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 the time it takes the two balls to collide and the height above the ground at which this collision occurs.

9b
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4 marks
(i)
Find the speed of each ball at the point when they collide.

(ii)
What can you deduce about the motion of the balls before and when they collide?

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