OCR
GCSE
Further Mathematics A
Y543/01: Mechanics
*1920696858*
A 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 pages 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 in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• 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 [603/1325/0] DC (DE/CB) 357860/3
OCR is an exempt Charity
Turn over
7ms on a smooth
-1
1 A particle P of mass 4 kg is moving in a straight line with a speed of
horizontal surface.
A constant force of magnitude 12 N acts on P for 5 seconds in the same direction
as P’s motion.
, 2
(a) Find the magnitude of the impulse exerted by the force on P. You must
include the units. [2]
(b) Hence determine the speed of P at the instant when the force stops acting.
[2]
(c) By considering the change in the kinetic energy of P, determine the work
done by the force
over the 5 seconds that it acts.
(d) Hence find the distance travelled by P while the force is acting on it. [2]
2 Dynamic viscosity is a physical property of liquids and is denoted by h.
The units of h are Ns /m2.
(a) Determine the dimensions of h. [3]
Kinematic viscosity is another physical property of liquids and is
denoted by o. h
Kinematic viscosity and dynamic viscosity are related by the formula o= where t
is the t density (mass per unit volume) of the liquid.
(b) By finding the dimensions of o, state a possible unit for o. [3] 3 In this
question you must show detailed reasoning.
A particle P of mass 3.25 kg is moving on a smooth horizontal plane with
velocity vms-1 where v = -4i 6j.
(a) Find the kinetic energy of P.
A system of horizontal forces starts to act on P. One of the forces is F N where F = -i
(3+t)j and t is the time, in seconds, after the system of forces starts to act.
(b) Find the power developed by F at time t = 0. [2]
(c) Given that the velocity of P does not change at any time, find the total power
developed by
the forces other than F at time t = 6.
4 Two particles, P of mass 2 kg and Q of mass 0.5 kg, are moving on a smooth horizontal
surface.
© OCR 2025 Y543/01 Jun25
, 3
Particle P is moving with speed 1.5ms-1 directly towards a vertical wall. Particle Q is
between P and the wall and is moving directly towards P with speed 3 5. ms-1 (see
diagram).
1.5 m s–1 3.5 m s–1
2 kg 0.5 kg
P Q
The particles collide directly. After the collision, P moves away from the wall with speed
0 3. ms-1. The coefficient of restitution between P and Q is denoted by e.
(a) Determine the value of e. [4]
After this collision, Q goes on to collide directly with the wall. The coefficient of
restitution between Q and the wall is e.
(b) Determine whether there will be a subsequent collision between P and Q.
[2] 5 One end of a light inextensible string of length 5 m is attached to a
fixed point A. The other end is attached to a particle P of mass m kg which lies on
a smooth horizontal plane.
With the string taut, P moves on the plane with constant speed vms-1 in a circular
path. The centre of the circular path is the point O which is 4 m vertically below A.
The string makes an angle of i with the downward vertical through A (see diagram).
A
θ
5m 4m
P O
(a) Given that the magnitude of the contact force between P and the surface is
equal to the
tension in the string, determine the value of v.
© OCR 2025 Y543/01 Jun25 Turn over
, 4
(b) Given instead that P is about to lose contact with the surface, determine the
angular velocity of P. [3]
6 One end of a light inextensible string of length r m is attached to a fixed point O. The
other end is attached to a particle P of mass m kg.
Particle P hangs in equilibrium vertically below O with the string taut. An initial
horizontal impulse is applied to P so that it instantaneously starts moving
horizontally with a speed of ums-1.
Particle P subsequently moves in complete circles in a vertical plane containing O.
When the line OP makes an angle of i with the downward vertical through O, the
speed of P is vms-1 and the tension in the string is T N.
(a) Show that T = mr ^u2 + +agr bgrcosih where a and b are constants to be
determined. [6]
(b) Determine, in terms of m, g and r, the minimum initial impulse required to
ensure that P
describes complete vertical circles around O with the string remaining taut.
7 A particle P of mass 36 kg moves in a straight line on a smooth horizontal plane. At
time t seconds the displacement of P from a fixed point O is x m and the velocity of
P is vms-1. Initially, P is at rest at O.
At time t = 0, P is acted on by a horizontal force, directed along the line. The
magnitude of the force is proportional to 9-v2. When v = 2.4, the magnitude of
the force is 32.4 N. When the velocity of P reaches 3ms-1, the force ceases to act.
(a) Show that while the force is acting the motion of P is modelled by the differential
equation
1 2 ddvt = 12.
9-v
(b) Hence find v in terms of t, showing that this expression for v is valid for 0
G Gt r. [5]
(c) Determine the total distance travelled by P in the interval 0 G Gt 10. Give
your answer in an exact form. [4]
© OCR 2025 Y543/01 Jun25
GCSE
Further Mathematics A
Y543/01: Mechanics
*1920696858*
A 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 pages 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 in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• 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 [603/1325/0] DC (DE/CB) 357860/3
OCR is an exempt Charity
Turn over
7ms on a smooth
-1
1 A particle P of mass 4 kg is moving in a straight line with a speed of
horizontal surface.
A constant force of magnitude 12 N acts on P for 5 seconds in the same direction
as P’s motion.
, 2
(a) Find the magnitude of the impulse exerted by the force on P. You must
include the units. [2]
(b) Hence determine the speed of P at the instant when the force stops acting.
[2]
(c) By considering the change in the kinetic energy of P, determine the work
done by the force
over the 5 seconds that it acts.
(d) Hence find the distance travelled by P while the force is acting on it. [2]
2 Dynamic viscosity is a physical property of liquids and is denoted by h.
The units of h are Ns /m2.
(a) Determine the dimensions of h. [3]
Kinematic viscosity is another physical property of liquids and is
denoted by o. h
Kinematic viscosity and dynamic viscosity are related by the formula o= where t
is the t density (mass per unit volume) of the liquid.
(b) By finding the dimensions of o, state a possible unit for o. [3] 3 In this
question you must show detailed reasoning.
A particle P of mass 3.25 kg is moving on a smooth horizontal plane with
velocity vms-1 where v = -4i 6j.
(a) Find the kinetic energy of P.
A system of horizontal forces starts to act on P. One of the forces is F N where F = -i
(3+t)j and t is the time, in seconds, after the system of forces starts to act.
(b) Find the power developed by F at time t = 0. [2]
(c) Given that the velocity of P does not change at any time, find the total power
developed by
the forces other than F at time t = 6.
4 Two particles, P of mass 2 kg and Q of mass 0.5 kg, are moving on a smooth horizontal
surface.
© OCR 2025 Y543/01 Jun25
, 3
Particle P is moving with speed 1.5ms-1 directly towards a vertical wall. Particle Q is
between P and the wall and is moving directly towards P with speed 3 5. ms-1 (see
diagram).
1.5 m s–1 3.5 m s–1
2 kg 0.5 kg
P Q
The particles collide directly. After the collision, P moves away from the wall with speed
0 3. ms-1. The coefficient of restitution between P and Q is denoted by e.
(a) Determine the value of e. [4]
After this collision, Q goes on to collide directly with the wall. The coefficient of
restitution between Q and the wall is e.
(b) Determine whether there will be a subsequent collision between P and Q.
[2] 5 One end of a light inextensible string of length 5 m is attached to a
fixed point A. The other end is attached to a particle P of mass m kg which lies on
a smooth horizontal plane.
With the string taut, P moves on the plane with constant speed vms-1 in a circular
path. The centre of the circular path is the point O which is 4 m vertically below A.
The string makes an angle of i with the downward vertical through A (see diagram).
A
θ
5m 4m
P O
(a) Given that the magnitude of the contact force between P and the surface is
equal to the
tension in the string, determine the value of v.
© OCR 2025 Y543/01 Jun25 Turn over
, 4
(b) Given instead that P is about to lose contact with the surface, determine the
angular velocity of P. [3]
6 One end of a light inextensible string of length r m is attached to a fixed point O. The
other end is attached to a particle P of mass m kg.
Particle P hangs in equilibrium vertically below O with the string taut. An initial
horizontal impulse is applied to P so that it instantaneously starts moving
horizontally with a speed of ums-1.
Particle P subsequently moves in complete circles in a vertical plane containing O.
When the line OP makes an angle of i with the downward vertical through O, the
speed of P is vms-1 and the tension in the string is T N.
(a) Show that T = mr ^u2 + +agr bgrcosih where a and b are constants to be
determined. [6]
(b) Determine, in terms of m, g and r, the minimum initial impulse required to
ensure that P
describes complete vertical circles around O with the string remaining taut.
7 A particle P of mass 36 kg moves in a straight line on a smooth horizontal plane. At
time t seconds the displacement of P from a fixed point O is x m and the velocity of
P is vms-1. Initially, P is at rest at O.
At time t = 0, P is acted on by a horizontal force, directed along the line. The
magnitude of the force is proportional to 9-v2. When v = 2.4, the magnitude of
the force is 32.4 N. When the velocity of P reaches 3ms-1, the force ceases to act.
(a) Show that while the force is acting the motion of P is modelled by the differential
equation
1 2 ddvt = 12.
9-v
(b) Hence find v in terms of t, showing that this expression for v is valid for 0
G Gt r. [5]
(c) Determine the total distance travelled by P in the interval 0 G Gt 10. Give
your answer in an exact form. [4]
© OCR 2025 Y543/01 Jun25
