OCR A Level Further Mathematics B (MEI)
Mechanics Major (Y421/01)
Oxford Cambridge and RSA
June 2026 – Afternoon
A Level Further Mathematics B (MEI)
Y421/01 Mechanics Major
Time allowed: 2 hours 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(MEI)
• a scientific or graphical calculator
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 your final answers to a degree of accuracy that is appropriate to the context.
• The acceleration due to gravity is denoted by g ms-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 120.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
, 2
Section A (33 marks)
1 A small box of mass 3 kg is pulled along a horizontal floor by a constant force of magnitude 35 N.
The force acts at an angle of i above the horizontal.
The total resistance to the motion of the box has magnitude 25 N.
The box starts from rest at a point O, and passes through a point 4 m from O with
speed 1.5 m s-1.
Use an energy method to determine the value of i. [3]
2
y
4
A 7m
2 B 2m
–4 –2 0 2 4 x
–2
C km
The diagram shows a system of three particles of masses 7m, 2m and km situated in the x-y plane
at the points A(-2, 3), B(4, 2) and C(1, -2) respectively.
The centre of mass of the three particles is at the point with coordinates (0, d).
(a) Find the value of k. [2]
(b) Find the value of d. [2]
, 3
JK32cos2tNO
3 At time t seconds, the total force acting on a particle P of mass 4 kg is K - 8 sin t O N.
K 0 O
L P
J 0 NO -1
When t = 0 the velocity of P is K O .
5 ms
KK O
6O
L P
(a) Find, in column vector form, the acceleration of P at time t seconds. [1]
(b) Determine the speed of P when t = 13 r. [5]
4
C
B
4m
50°
A
A uniform rod AB of mass 3 kg and length 4 m rests with one end A on rough horizontal ground.
A light inextensible string has one end attached to the rod at B and the other end attached to a
fixed point C.
The string is perpendicular to the rod and lies in the same vertical plane as the rod. The rod is in
equilibrium, inclined at 50° to the ground, as shown in the diagram.
(a) Complete the diagram in the Printed Answer Booklet to show all the forces acting on the
rod. [1]
(b) By taking moments about A, find the tension in the string. [2]
(c) Determine the magnitude of the total contact force between the rod and the ground. [4]
Turn over
, 4
dr r
5 In this question you may assume that if r and s are any physical quantities then ; E = ; E.
ds s
You may also assume that all given numerical constants are dimensionless.
(a) Find the dimensions of power. [1]
A car of mass m moves horizontally in a straight line. When the car is a distance x from a point O,
it is moving away from O with speed v.
The power developed by the car is P. The maximum possible speed of the car during its motion
is U.
The differential equation for the motion of the car is given by
dv J vd NO
ma v b c K
.
d x = P K1 - U3O
L P
(b) Explain why d = 3. [1]
dv
(c) Show that the dimensions of are T-1. [1]
dx
(d) Use dimensional analysis to determine the values of a, b and c. [3]
Once the car attains a speed of 12 U , the power developed by the car is immediately reduced to
zero.
A student calculates that the time taken, t, for the speed of the car to reduce from 1 U to 1 U is
2 4
2mU2
given by t =
P .
(e) Determine whether this expression for t is dimensionally consistent. [2]
Mechanics Major (Y421/01)
Oxford Cambridge and RSA
June 2026 – Afternoon
A Level Further Mathematics B (MEI)
Y421/01 Mechanics Major
Time allowed: 2 hours 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(MEI)
• a scientific or graphical calculator
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 your final answers to a degree of accuracy that is appropriate to the context.
• The acceleration due to gravity is denoted by g ms-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 120.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
, 2
Section A (33 marks)
1 A small box of mass 3 kg is pulled along a horizontal floor by a constant force of magnitude 35 N.
The force acts at an angle of i above the horizontal.
The total resistance to the motion of the box has magnitude 25 N.
The box starts from rest at a point O, and passes through a point 4 m from O with
speed 1.5 m s-1.
Use an energy method to determine the value of i. [3]
2
y
4
A 7m
2 B 2m
–4 –2 0 2 4 x
–2
C km
The diagram shows a system of three particles of masses 7m, 2m and km situated in the x-y plane
at the points A(-2, 3), B(4, 2) and C(1, -2) respectively.
The centre of mass of the three particles is at the point with coordinates (0, d).
(a) Find the value of k. [2]
(b) Find the value of d. [2]
, 3
JK32cos2tNO
3 At time t seconds, the total force acting on a particle P of mass 4 kg is K - 8 sin t O N.
K 0 O
L P
J 0 NO -1
When t = 0 the velocity of P is K O .
5 ms
KK O
6O
L P
(a) Find, in column vector form, the acceleration of P at time t seconds. [1]
(b) Determine the speed of P when t = 13 r. [5]
4
C
B
4m
50°
A
A uniform rod AB of mass 3 kg and length 4 m rests with one end A on rough horizontal ground.
A light inextensible string has one end attached to the rod at B and the other end attached to a
fixed point C.
The string is perpendicular to the rod and lies in the same vertical plane as the rod. The rod is in
equilibrium, inclined at 50° to the ground, as shown in the diagram.
(a) Complete the diagram in the Printed Answer Booklet to show all the forces acting on the
rod. [1]
(b) By taking moments about A, find the tension in the string. [2]
(c) Determine the magnitude of the total contact force between the rod and the ground. [4]
Turn over
, 4
dr r
5 In this question you may assume that if r and s are any physical quantities then ; E = ; E.
ds s
You may also assume that all given numerical constants are dimensionless.
(a) Find the dimensions of power. [1]
A car of mass m moves horizontally in a straight line. When the car is a distance x from a point O,
it is moving away from O with speed v.
The power developed by the car is P. The maximum possible speed of the car during its motion
is U.
The differential equation for the motion of the car is given by
dv J vd NO
ma v b c K
.
d x = P K1 - U3O
L P
(b) Explain why d = 3. [1]
dv
(c) Show that the dimensions of are T-1. [1]
dx
(d) Use dimensional analysis to determine the values of a, b and c. [3]
Once the car attains a speed of 12 U , the power developed by the car is immediately reduced to
zero.
A student calculates that the time taken, t, for the speed of the car to reduce from 1 U to 1 U is
2 4
2mU2
given by t =
P .
(e) Determine whether this expression for t is dimensionally consistent. [2]
