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Constant Acceleration 1D
Question Paper 2
Level
A Level
Subject
Maths
Exam Board
AQA
Module
Mechanics 1
Topic
Motion
Sub Topic
Constant Acceleration 1D
Booklet
Question Paper - 2
Time Allowed:
56 minutes
Score:
/46
Percentage:
/100
Grade Boundaries:
A*
>85%
A
777.5%
B
C
D
E
U
70%
62.5%
57.5%
45%
<45%
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Q1.
A pair of cameras records the time that it takes a car on a motorway to travel a distance of
2000 metres. A car passes the first camera whilst travelling at 32 m s–1.
The car continues at this speed for 12.5 seconds and then decelerates uniformly until it passes the
second camera when its speed has decreased to 18 m s–1.
(a)
Calculate the distance travelled by the car in the first 12.5 seconds.
(1)
(b)
Find the time for which the car is decelerating.
(3)
(c)
Sketch a speed–time graph for the car on this 2000-metre stretch of motorway.
(3)
(d)
Find the average speed of the car on this 2000-metre stretch of motorway.
(2)
(Total 9 marks)
Q2.
A ball is thrown vertically upwards at a speed of 4.9 m s–1 from a height of 1 metre
above ground level. The ball is caught when it returns to a height of 1 metre above ground
level and is travelling downwards.
(a)
Find the time that it takes for the ball to reach its maximum height.
(3)
(b)
Find the maximum height of the ball above ground level.
(3)
(c)
State the total time for which the ball is moving.
(1)
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(d)
State the speed of the ball when it is caught.
(1)
(Total 8 marks)
Q3.
A sprinter accelerates from rest at a constant rate for the first 10 metres of a
100-metre race. He takes 2.5 seconds to run the first 10 metres.
(a)
Find the acceleration of the sprinter during the first 2.5 seconds of the race.
(3)
(b)
Show that the speed of the sprinter at the end of the first 2.5 seconds of the race
is 8 m s–1.
(2)
(c)
The sprinter completes the 100-metre race, travelling the remaining 90 metres at a
constant speed of 8 m s–1. Find the total time taken for the sprinter to travel the
100 metres.
(3)
(d)
Calculate the average speed of the sprinter during the 100-metre race.
(2)
(Total 10 marks)
Q4.A box of mass 4 kg is held at rest on a plane inclined at an angle of 40° to the horizontal.
The box is then released and slides down the plane.
(a)
A simple model assumes that the only forces acting on the box are its weight and
the normal reaction from the plane. Show that, according to this simple model, the
acceleration of the box would be 6.30 m s−2, correct to three significant figures.
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(3)
(b)
In fact, the box moves down the plane with constant acceleration and travels 0.9
metres in 0.6 seconds. By using this information, find the acceleration of the box.
(3)
(c)
Explain why the answer to part (b) is less than the answer to part (a).
(1)
(Total 7 marks)
Q5.
A motorcycle and rider, of total mass 300 kg, are accelerating in a straight line along
a horizontal road at 2.2 m s–2.
(a)
Show that the magnitude of the resultant force acting on the motorcycle is 660 N.
(1)
(b)
A forward driving force of P newtons together with a resistance force of magnitude
400 newtons act on the motorcycle. Find P.
(2)
(c)
Find the time that it would take for the speed of the motorcycle to increase from 12
m s–1 to 23 m s–1.
(3)
(Total 6 marks)
Q6.
A lift is travelling upwards and accelerating uniformly. During a 5 second period, it
travels 16 metres and the speed of the lift increases from u m s–1 to 4.2 m s–1.
(a)
Find u.
(3)
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(b)
Find the acceleration of the lift.
(3)
(Total 6 marks)
Page 5