# WME01 Mechanics 1 (M1) January 2025 Paper 01

Pearson Edexcel International A Level WME01 Mechanics 1 (M1) past paper 01, January 2025. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wme01/2025-january-paper-01/
- PDF: https://mathvsarham.com/papers/wme01/WME01_january_2025_paper_01_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International A Level
- Subject: WME01 Mechanics 1 (M1) (https://mathvsarham.com/past-papers/wme01/)
- Session: January 2025
- Paper: 01
- Component code: WME01/01
- Time allowed: 90 minutes
- Total marks: 75
- Pages: 25

## Question paper text

Extracted automatically from the PDF; diagrams are missing and notation may be imperfect.

Question 1
A particle of mass 2.5 kg moves on a smooth horizontal plane under the action of three horizontal forces, F_1, F_2 and F_3, where
[Diagram or table: see page 3 of the paper]
(a) Find the magnitude of the acceleration of the particle. [4]
A fourth force, F_4 = ( pi + pj) N, where p is a constant, is added.
The resultant of the four forces acts in the direction of the vector (7i + 2j).
(b) Find the value of p. [4]

Question 2
The fixed points A, B and C lie in a straight line on a horizontal road.
• At time t = 0, a motorbike passes through A with speed 5 m s^–1
• From A, the motorbike accelerates uniformly until it reaches B with a speed of V m s^–1
• The motorbike takes T_1 seconds to travel from A to B
• From B, the motorbike decelerates uniformly until it comes to rest at C
• The motorbike takes T_2 seconds to travel from B to C
(a) Sketch a speed‑time graph for the motion of the motorbike as it moves from A to C. [3]
The distance AB is 132 m and the distance BC is 136 m.
(b) Find, in terms of V, an expression for
(i) T_1
(ii) T_2 [4]
Given that the motorbike takes 28 s to travel from A to C,
(c) find the value of V, [2]
(d) find the deceleration of the motorbike. [2]

Question 3
[Diagram or table: see page 9 of the paper]
A particle P of mass 3m kg and a particle Q of mass m kg are at rest on a rough horizontal surface. The distance between P and Q is 1.4 m, as shown in Figure 1.
An impulse of magnitude λ N s is now applied to P in the direction PQ. Immediately after the impulse is applied, the speed of P is 5 m s^–1
(a) Find λ in terms of m. [2]
Immediately before P collides with Q, the speed of P is 2.5 m s^–1 The coefficient of friction between P and the surface is μ
(b) Find the value of μ [7]
Immediately after P collides with Q, the speed of Q is 2.1 m s^–1
(c) Find the speed of P immediately after the collision. [3]

Question 4
[Diagram or table: see page 13 of the paper]
A uniform rod AB has length 3 m and weight W newtons. The rod is suspended by two light vertical ropes. One rope is attached to the rod at A and the other rope is attached to the rod at C, where AC = 2.1 m.
The rod is in equilibrium in a horizontal position, as shown in Figure 2.
The tension in the rope at C is 350 N.
(a) Show that W = 490 [3]
A particle P of weight 210 N is attached to the rod at a distance d metres from A. The tension in the rope at C is now 600 N. The rod remains in equilibrium in a horizontal position.
(b) Find the value of d. [3]
Particle P is removed from the rod. A particle Q of weight X newtons is now attached at B. The rod remains in equilibrium in a horizontal position and is now on the point of tilting.
(c) Find the value of X. [4]

Question 5
[In this question i and j are horizontal perpendicular unit vectors and position vectors are given relative to a fixed origin.]
In a game, a ball B is rolled across a horizontal surface towards a fixed target. The ball is modelled as a particle moving with constant velocity.
At time t = 1 s, the position vector of B is (–2i + 5j) m. At time t = 9 s, the position vector of B is (10i – 3j) m.
(a) Find the velocity of the ball. [3]
The position vector of the target is (13i – 5j) m.
(b) Use the model to find the distance of B from the target at time t = 7 s. [4]

Question 6
[Diagram or table: see page 19 of the paper]
A particle P of mass m is held in equilibrium on a fixed rough inclined plane by a light inextensible string.
The plane is inclined at an angle α to the horizontal, where α < 45° The string is inclined to the plane at angle α, as shown in Figure 3.
The string lies in a vertical plane that contains a line of greatest slope of the inclined plane.
When the tension in the string is 0.75 mg, P is on the point of moving up the plane.
(a) Find an expression for the magnitude of the frictional force acting on P, giving your answer in terms of m, g and α. [3]
The coefficient of friction between P and the plane is 1/2
(b) Show that
[Diagram or table: see page 19 of the paper]
[6]
The string breaks.
(c) Determine whether P remains at rest. You must justify your reasoning. [3]

Question 7
[Diagram or table: see page 23 of the paper]
One end of a light inextensible string is attached to a particle A of mass 2m. The other end is attached to a particle B of mass 3m. The string passes over a small smooth fixed pulley. The string is taut and both straight parts of the string are vertical. Both particles are held at a distance 0.5 m above a horizontal surface, as shown in Figure 4.
The system is released from rest and B moves downwards.
(a) Find the tension in the string in terms of m and g. [5]
(b) Find the speed of B at the instant it strikes the surface. [4]
In the subsequent motion, A does not reach the pulley and B does not rebound after it strikes the surface.
(c) Find the time from the instant when the system is released from rest to the instant when A first reaches a height of 1.06 m above the surface. [6]