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Candidate surname Other names Centre Number Candidate Number Afternoon Marks
• Use^ black^ ink^ or^ ball‑point^ pen.
Advice
• The^ marks^ for^ each^ question^ are^ shown^ in^ brackets
• Fill^ in^ the^ boxes^ at^ the^ top^ of^ this^ page^ with^ your^ name,
• Try^ to^ answer^ every^ question.
• A^ booklet^ ‘Mathematical^ Formulae^ and^ Statistical^ Tables’^ is^ provided.
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Mathematics
Advanced
PAPER 32: Mechanics
Candidates may use any calculator allowed by Pearson regulations. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them.
Instructions
• If^ pencil^ is^ used^ for^ diagrams/sketches/graphs^ it^ must^ be^ dark^ (HB^ or^ B).
centre number and candidate number. Answer all questions and ensure that your answers to parts of questions are clearly labelled. Answer the questions in the spaces provided
- there may be more space than you need. You should show sufficient working to make your methods clear. Answers without working may not gain full credit. Unless otherwise indicated, whenever a value of g is required, take g = 9.8 m s−^2 and give your answer to either 2 significant figures or 3 significant figures.
• The^ total^ mark^ for^ this^ part^ of^ the^ examination^ is^ 50.^ There^ are^6 questions.
- use this as a guide as to how much time to spend on each question.
• Read^ each^ question^ carefully^ before^ you^ start^ to^ answer^ it.
• Check^ your^ answers^ if^ you^ have^ time^ at^ the^ end.
Information
EDEXCEL A LEVEL MATHEMATICS (9MA0/ 32 ) QUESTION PAPER 32 AND MARK SCHEME SUMMER 2025
1. A car moves in a straight line along a horizontal road with constant acceleration 2 m s–^2 The car is moving with speed 15 m s–^1 in the direction of the acceleration when it passes a signpost on the road. The car is modelled as a particle. (a) Use the model to find the speed of the car 4 s after passing the signpost. Figure 1 below shows the horizontal forces acting on the car. Given that
- the car has mass 800 kg
- the driving force of the engine has magnitude D newtons
- the resistance to the motion of the car has magnitude 400 N
- the acceleration of the car is 2 m s–^2 in the direction of the driving force (b) use the model to find the value of D. 2 m s–^2
400 N
2
D N
800 kg Figure 1 ■■■■
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B (2 kg)
5 N
α Figure 2 A small box B of mass 2 kg is dragged in a straight line, along a rough horizontal plane, at a constant speed by a force of magnitude 5 N. 3 The line of action of the force makes an angle α with the plane, where sin α = 5
as shown in Figure 2. (a) Show that the magnitude of the normal reaction of the plane on the box is 16.6 N. At the instant when B is at the point O on the plane, the force of magnitude 5 N is removed. (b) Describe the motion of the box after the force of magnitude 5 N is removed. (c) Find the magnitude of the normal reaction of the plane on the box after the force of magnitude 5 N is removed. Given that after the force of magnitude 5 N is removed
- the box is modelled as a particle
- air resistance is modelled as being negligible
- the coefficient of friction between the box and the plane is modelled as 0.
- the speed of the box as it passes through O is 4 m s–^1
- the box comes to rest at the point X on the plane (d) use the model to find the length OX. (e) State one limitation of the model, apart from ignoring air resistance, that could affect your answer to part (d). 4
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Question 2 continued ■■■■ 5 Turn over
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Question 2 continued ■■■■ (Total for Question 2 is 10 marks) 7 Turn over
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3. [ In this question, i and j are horizontal unit vectors due east and due north respectively .] A particle P of mass 0.5 kg moves with constant acceleration (2 i – 2.4 j ) m s–^2 on a smooth horizontal plane under the action of a constant horizontal force F N. (a) Find F in terms of i and j. At time t = 0, P is moving with velocity (– 7 i + 7.8 j ) m s–^1 (b) Find the velocity of P at time t = 2 seconds. (c) Find the direction of motion of P at time t = 2 seconds, giving your answer as a bearing in degrees. At time t = 0, P passes through the point O. At time t = 5 seconds, P passes through the point A. → (d) Find OA in terms of i and j. 8
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Question 3 continued 10 ■■■■
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Question 3 continued ■■■■ (Total for Question 3 is 8 marks) 11 Turn over
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Question 4 continued ■■■■ 13 Turn over
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Question 4 continued 14 ■■■■
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14 m s–^1 O (^) θ H m N A 40 m Figure 3 A small stone is projected with speed 14 m s–^1 from a point O on the top of a cliff. The point O is H metres vertically above the point N. Point N is on horizontal ground. 1 The stone is projected at an angle θ above the horizontal, where tan θ = 2 The stone strikes the horizontal ground at the point A , where NA = 40 m, as shown in Figure 3. The stone is modelled as a particle moving freely under gravity. Using this model, find (a) the value of H (b) the maximum height of the stone above the horizontal ground. 16
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Question 5 continued ■■■■ 17 Turn over
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Question 5 continued ■■■■ (Total for Question 5 is 8 marks) 19 Turn over
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B
α C (2 M ) A Figure 4 A uniform rod AB has mass M and length 2 a. A particle of mass 2 M is attached to the rod at the point C , where AC = 0.5 a The rod rests with end A on rough horizontal ground and end B against a vertical wall. The rod lies in a vertical plane which is perpendicular to the wall. The rod is in equilibrium at an angle α to the wall, as shown in Figure 4. In an initial model
- the vertical wall is modelled as being smooth
- the magnitude of the normal reaction of the ground on the rod at A is R
- the magnitude of the force exerted on the rod by the wall at B is S Using the model, (a) find R in terms of M and g (b) show that S = Mg tan α In a refined model
- the vertical wall is modelled as being rough
- the^ magnitude^ of^ the^ normal^ reaction^ of^ the^ ground^ on^ the^ rod^ at^ A^ is^ R 1 (c) State which is greater, R or R 1 , giving a reason for your answer. 20
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