Oxford Cambridge and RSA
GCSE
Further Mathematics A
Y533/01: Mechanics
*1919889125*
AS Level
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined page at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [T/508/5499] DC (ST/CB) 357853/5
OCR is an exempt Charity
Turn over
1 A cricket ball of mass 0.16 kg is at rest on rough horizontal ground when it is struck
by a bat.
Immediately after the ball is struck its speed is 15ms-1 in a horizontal direction.
(a) Find the magnitude of the impulse exerted by the bat on the ball. [1]
, 2
The ball remains in contact with the ground and the resistance to the motion of the
ball is modelled as constant.
The ball comes to rest again after it has travelled 30 m along the ground.
(b) Use the work-energy principle to find the magnitude of the resistance to the
motion of the ball. [3]
2 Two particles, A of mass m kg and B of mass 2m kg, are connected by a light
inextensible string. The particles are initially placed together at rest on a smooth
horizontal surface with the string slack.
At a certain instant, A and B are projected along the surface, directly away from
each other, with speeds of 3ms-1 and ums-1 respectively. You are given that u11 5. .
(a) Find, in terms of u, the speed of A immediately after the string becomes taut.
[2]
(b) (i) State the direction of motion of B immediately after the string becomes
taut. [1]
(ii)
Find, in terms of m and u, the magnitude of the impulse exerted on
B as a result of the
string becoming taut.
(iii) Write down an expression for the impulse exerted on A as a result
of the string becoming taut. [1] m(3+u)2
(c) Show that the loss of kinetic energy as a result of the string becoming taut is
3 J. [3] 3 A car of mass 900 kg has an engine that is capable
of working at a maximum power of 12 kW.
When the car is travelling along a straight horizontal road, the maximum constant speed
that it can maintain is 40ms-1.
In an initial model of the motion of the car it is assumed that the total resistance to
motion is constant.
(a) (i) Show that when the car is travelling at 15ms-1 along the horizontal
road with the engine working at a constant rate of 10 kW, the acceleration
of the car is 0 407. ms-2 correct to
3 significant figures. [3]
(ii) Find the speed of the car when it is accelerating at 0 2. ms-2 along the
horizontal road
with the engine working at a constant rate of 9.6 kW.
© OCR 2025 Y533/01 Jun25
, 3
(iii) The car now starts to descend a straight road which is inclined at 1° to
the horizontal.
Find the power produced by the engine of the car when it is travelling
along this road at a constant speed of 40ms-1. [2]
In a refined model of the motion of the car it is assumed that the total resistance to
motion is proportional to the speed of the car.
(b) (i) Show that the total resistance to the motion of the car is now given by 7.5
where
vms-1 is the speed of the car.
(ii) State one way in which the refined model is an improvement over the initial
model. [1]
(iii) Find, according to the refined model, the speed of the car when it is accelerating
at 0 2. ms-2 along the horizontal road with the engine working at a constant rate of
9.6 kW.
4 Two particles, A of mass 4 kg and B of mass 2 kg, are free to move along the same
straight line on a smooth horizontal surface. They are projected directly towards
each other with speeds of 6ms-1 and 5ms-1 respectively.
After A and B collide the speed of A is 1ms-1.
(a) Determine the possible values of the coefficient of restitution between A and
B. [6]
(b) State whether the collision between A and B is perfectly elastic. Justify your
answer. [1]
Turn over
5 One end of a light inextensible string of length d m is attached to a particle B of
mass m kg. The other end of the string is attached to a fixed point O on a smooth
horizontal plane.
© OCR 2025 Y533/01 Jun25
, 4
Particle B moves on the plane with constant speed ums-1 in a horizontal circle with
centre O (see diagram).
O dm
B u m s–1
m kg
The period, which is the time taken for B to complete one revolution, is denoted by
p seconds and the tension in the string is F N.
(a) Use dimensional analysis to derive a formula for F in terms of d, m and p.
You should define any other symbols used in your formula for F. [4]
(b) Explain why it was not necessary to consider the quantity u in the analysis
in part (a). [1]
(c) Instead, use Newton’s second law to derive a formula for F in terms of d, m
and p. [3]
(d) Considering your answers to part (a) and part (c), state one disadvantage of
using
dimensional analysis to derive a formula for F.
6 A disc of mass 2 kg is projected, with initial speed 16 4. ms-1, directly up a rough
plane which is inclined at an angle of 15° to the horizontal. The coefficient of
friction between the plane and the disc is 0.2.
(a) (i) Determine the average power generated by the frictional force in the first
3 seconds of
the disc’s motion.
(ii) Explain the significance of the sign of your answer to part (a)(i).
(b) Use an energy method to find the distance the disc travels up the plane
from the point where
it is projected to the point where it comes to instantaneous rest.
7 In this question you must show detailed reasoning.
© OCR 2025 Y533/01 Jun25
GCSE
Further Mathematics A
Y533/01: Mechanics
*1919889125*
AS Level
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined page at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [T/508/5499] DC (ST/CB) 357853/5
OCR is an exempt Charity
Turn over
1 A cricket ball of mass 0.16 kg is at rest on rough horizontal ground when it is struck
by a bat.
Immediately after the ball is struck its speed is 15ms-1 in a horizontal direction.
(a) Find the magnitude of the impulse exerted by the bat on the ball. [1]
, 2
The ball remains in contact with the ground and the resistance to the motion of the
ball is modelled as constant.
The ball comes to rest again after it has travelled 30 m along the ground.
(b) Use the work-energy principle to find the magnitude of the resistance to the
motion of the ball. [3]
2 Two particles, A of mass m kg and B of mass 2m kg, are connected by a light
inextensible string. The particles are initially placed together at rest on a smooth
horizontal surface with the string slack.
At a certain instant, A and B are projected along the surface, directly away from
each other, with speeds of 3ms-1 and ums-1 respectively. You are given that u11 5. .
(a) Find, in terms of u, the speed of A immediately after the string becomes taut.
[2]
(b) (i) State the direction of motion of B immediately after the string becomes
taut. [1]
(ii)
Find, in terms of m and u, the magnitude of the impulse exerted on
B as a result of the
string becoming taut.
(iii) Write down an expression for the impulse exerted on A as a result
of the string becoming taut. [1] m(3+u)2
(c) Show that the loss of kinetic energy as a result of the string becoming taut is
3 J. [3] 3 A car of mass 900 kg has an engine that is capable
of working at a maximum power of 12 kW.
When the car is travelling along a straight horizontal road, the maximum constant speed
that it can maintain is 40ms-1.
In an initial model of the motion of the car it is assumed that the total resistance to
motion is constant.
(a) (i) Show that when the car is travelling at 15ms-1 along the horizontal
road with the engine working at a constant rate of 10 kW, the acceleration
of the car is 0 407. ms-2 correct to
3 significant figures. [3]
(ii) Find the speed of the car when it is accelerating at 0 2. ms-2 along the
horizontal road
with the engine working at a constant rate of 9.6 kW.
© OCR 2025 Y533/01 Jun25
, 3
(iii) The car now starts to descend a straight road which is inclined at 1° to
the horizontal.
Find the power produced by the engine of the car when it is travelling
along this road at a constant speed of 40ms-1. [2]
In a refined model of the motion of the car it is assumed that the total resistance to
motion is proportional to the speed of the car.
(b) (i) Show that the total resistance to the motion of the car is now given by 7.5
where
vms-1 is the speed of the car.
(ii) State one way in which the refined model is an improvement over the initial
model. [1]
(iii) Find, according to the refined model, the speed of the car when it is accelerating
at 0 2. ms-2 along the horizontal road with the engine working at a constant rate of
9.6 kW.
4 Two particles, A of mass 4 kg and B of mass 2 kg, are free to move along the same
straight line on a smooth horizontal surface. They are projected directly towards
each other with speeds of 6ms-1 and 5ms-1 respectively.
After A and B collide the speed of A is 1ms-1.
(a) Determine the possible values of the coefficient of restitution between A and
B. [6]
(b) State whether the collision between A and B is perfectly elastic. Justify your
answer. [1]
Turn over
5 One end of a light inextensible string of length d m is attached to a particle B of
mass m kg. The other end of the string is attached to a fixed point O on a smooth
horizontal plane.
© OCR 2025 Y533/01 Jun25
, 4
Particle B moves on the plane with constant speed ums-1 in a horizontal circle with
centre O (see diagram).
O dm
B u m s–1
m kg
The period, which is the time taken for B to complete one revolution, is denoted by
p seconds and the tension in the string is F N.
(a) Use dimensional analysis to derive a formula for F in terms of d, m and p.
You should define any other symbols used in your formula for F. [4]
(b) Explain why it was not necessary to consider the quantity u in the analysis
in part (a). [1]
(c) Instead, use Newton’s second law to derive a formula for F in terms of d, m
and p. [3]
(d) Considering your answers to part (a) and part (c), state one disadvantage of
using
dimensional analysis to derive a formula for F.
6 A disc of mass 2 kg is projected, with initial speed 16 4. ms-1, directly up a rough
plane which is inclined at an angle of 15° to the horizontal. The coefficient of
friction between the plane and the disc is 0.2.
(a) (i) Determine the average power generated by the frictional force in the first
3 seconds of
the disc’s motion.
(ii) Explain the significance of the sign of your answer to part (a)(i).
(b) Use an energy method to find the distance the disc travels up the plane
from the point where
it is projected to the point where it comes to instantaneous rest.
7 In this question you must show detailed reasoning.
© OCR 2025 Y533/01 Jun25
