Newton’s laws of motion: past paper questions

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• Question 2May/June 2026, paper 41Structured6 marks

  A car of mass $1200\text{ kg}$ is moving on a straight horizontal road. The resistance to the motion of the car has a constant magnitude of $600\text{ N}$ and the car's engine is working at a rate of $27\text{ kW}$.

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• Question 1Oct/Nov 2025, paper 41Structured4 marks

  A car of mass $900\text{ kg}$ is moving along a straight horizontal road against a constant resistance to motion of $350\text{ N}$. At an instant when the car is moving at $15{\text{ ms}}^{-1}$ its acceleration is $0.25{\text{ ms}}^{-2}$.

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• Question 1Oct/Nov 2024, paper 41Structured4 marks

  Two particles, of masses $1.8\text{ kg}$ and $1.2\text{ kg}$, are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang vertically. The system is released from rest.

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• Question 4Oct/Nov 2023, paper 41Structured9 marks

  Two particles $P$ and $Q$, of masses $6\text{ kg}$ and $2\text{ kg}$ respectively, lie at rest $12.5\text{ m}$ apart on a rough horizontal plane. The coefficient of friction between each particle and the plane is $0.4$.

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• Question 4May/June 2026, paper 41Structured10 marks

  Three particles $A$, $B$ and $C$ have masses $3\text{ kg}$, $1.5\text{ kg}$ and $m\text{ kg}$ respectively, where $m>1.5$. Particles $A$ and $B$ are attached to the ends of a light inextensible string that passes over a smooth fixed pulley.

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• Question 8Oct/Nov 2025, paper 41Structured8 marksHas a diagram

  A block $A$ of mass $2\text{ kg}$ and a particle $B$ of mass $0.5\text{ kg}$ are connected by a light inextensible string inclined at ${15}^{\circ }$ to the horizontal.

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• Question 7Oct/Nov 2024, paper 41Structured8 marks

  A car has mass $1200\text{ kg}$. When the car is travelling at a speed of $v{\text{ ms}}^{-1}$, there is a resistive force of magnitude $kv\text{ N}$. The maximum power of the car’s engine is $92.16\text{ kW}$.

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• Question 6Oct/Nov 2023, paper 41Structured9 marks

  A car of mass $1300\text{ kg}$ is moving on a straight road. On a horizontal section of the road, the car has a constant speed of $30{\text{ m s}}^{-1}$ and there is a constant force of $650\text{ N}$ resisting the motion.

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• Question 5May/June 2026, paper 41Structured10 marksHas a diagram

  A particle of mass $3.6\text{ kg}$ is placed on a rough plane inclined at an angle of ${30}^{\circ }$ to the horizontal. The particle is held at rest on the plane by a horizontal force of magnitude $24\sqrt{3}\text{ N}$.

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• Question 2Oct/Nov 2025, paper 42Structured5 marks

  A railway locomotive of mass $240000\text{ kg}$ is towing a coach of mass $36000\text{ kg}$ down a hill inclined at an angle of ${\sin }^{-1}0.04$ to the horizontal.

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• Question 3Oct/Nov 2024, paper 42Structured5 marks

  A cyclist is riding along a straight horizontal road. The total mass of the cyclist and his bicycle is $90\mathrm{k}\mathrm{g}$. The power exerted by the cyclist is $250\mathrm{W}$.

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• Question 4Oct/Nov 2023, paper 42Structured7 marks

  A particle $P$ of mass $0.2\text{ kg}$ lies at rest on a rough horizontal plane. A horizontal force of $1.2\text{ N}$ is applied to $P$. Given that $P$ is in limiting equilibrium, find the coefficient of friction between $P$ and the plane.

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• Question 1May/June 2026, paper 42Structured4 marks

  A car of mass $960\text{ kg}$ is moving on a straight horizontal road. There is a constant force of magnitude $620\text{ N}$ resisting the motion of the car. Calculate the power developed by the engine of the car when it is moving at a constant speed of $25{\text{ ms}}^{-1}$.

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• Question 5Oct/Nov 2025, paper 42Structured6 marksHas a diagram

  A block of mass $5\text{ kg}$ is being pulled straight down a line of greatest slope of a rough plane by a force of magnitude $20\text{ N}$.

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• Question 7Oct/Nov 2024, paper 42Structured11 marksHas a diagram

  Two particles, $A$ and $B$, of masses $0.2\mathrm{k}\mathrm{g}$ and $0.3\mathrm{k}\mathrm{g}$ respectively, are attached to the ends of a light inextensible string.

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• Question 6Oct/Nov 2023, paper 42Structured9 marks

  A railway engine of mass $120000\text{ kg}$ is towing a coach of mass $60000\text{ kg}$ up a straight track inclined at an angle of $\alpha$ to the horizontal where $\sin \alpha =0.02$. There is a light rigid coupling, parallel to the track, connecting the engine and coach.

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• Question 3May/June 2026, paper 42Structured10 marksHas a diagram

  Two particles, $A$ and $B$, of masses $0.5\text{ kg}$ and $0.8\text{ kg}$ respectively are attached to the ends of a light inextensible string. The string passes over a small smooth pulley fixed at the end of a rough horizontal plane and to the top of a smooth inclined plane.

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• Question 2Oct/Nov 2025, paper 43Structured6 marks

  The engine of a motorcycle can generate a maximum power of $105\text{ kW}$. The mass of the motorcycle and its rider is $400\text{ kg}$.

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• Question 3Oct/Nov 2024, paper 43Structured6 marks

  A car of mass $1600\text{ kg}$ travels up a slope inclined at an angle of ${\sin }^{-1}0.08$ to the horizontal. There is a constant resistance of magnitude $240\text{ N}$ acting on the car. It is given that the car travels at a constant speed of $32\text{ m}{\text{s}}^{-1}$.

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• Question 3Oct/Nov 2023, paper 43Structured6 marks

  A block of mass $8\text{ kg}$ slides down a rough plane inclined at ${30}^{\circ }$ to the horizontal, starting from rest. The coefficient of friction between the block and the plane is $\mu$. The block accelerates uniformly down the plane at $2.4\text{ m}{\text{ s}}^{-2}$.

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• Question 6May/June 2026, paper 42Structured8 marksHas a diagram

  A crate of weight $W\text{ N}$ is at rest on rough horizontal ground. The crate is pulled at a constant acceleration of $1.5{\text{ ms}}^{-2}$ along the ground in a straight line by a light rope.

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• Question 5Oct/Nov 2025, paper 43Structured10 marks

  Particles $A$ and $B$, of masses $2\text{ kg}$ and $6\text{ kg}$ respectively, are attached to the ends of a light inextensible string. The string passes over a smooth fixed pulley and the particles hang vertically below the pulley.

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• Question 5Oct/Nov 2024, paper 43Structured8 marks

  A particle of mass $12\text{ kg}$ is going to be pulled across a rough horizontal plane by a light inextensible string. The string is at an angle of ${30}^{\circ }$ above the plane and has tension $T\text{ N}$ (see diagram).

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• Question 7Oct/Nov 2023, paper 43Structured13 marksHas a diagram

  Particles $A$ and $B$, of masses $2.4\text{ kg}$ and $3.3\text{ kg}$ respectively, are connected by a light inextensible string that passes over a smooth pulley which is fixed to the top of a rough plane. The plane makes an angle of ${\theta }^{\circ }$ with horizontal ground.

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• Question 3May/June 2026, paper 43Structured4 marks

  A block of mass $m\mathrm{k}\mathrm{g}$ is pulled up a rough plane inclined at an angle of ${30}^{\circ }$ to the horizontal by a constant force of magnitude $20\mathrm{N}$. This force acts parallel to a line of greatest slope of the plane.

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• Question 1May/June 2025, paper 41Structured4 marksHas a diagram

  A block of mass $12\text{ kg}$ is being pulled by a rope up a rough plane. The plane is inclined at an angle of ${20}^{\circ }$ above the horizontal. The rope pulling the block is parallel to a line of greatest slope of the plane.

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• Question 7Oct/Nov 2024, paper 43Structured10 marksHas a diagram

  Two particles, $A$ and $B$, of masses $3\text{ kg}$ and $5\text{ kg}$ respectively, are connected by a light inextensible string that passes over a fixed smooth pulley. The particles are held with the string taut and its straight parts vertical.

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• Question 6May/June 2023, paper 41Structured8 marksHas a diagram

  Two particles $P$ and $Q$, of masses $0.2\text{ kg}$ and $0.1\text{ kg}$ respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley at $B$ which is attached to two inclined planes.

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• Question 5May/June 2026, paper 43Structured10 marks

  A lorry of mass $13500\mathrm{k}\mathrm{g}$ is towing a trailer of mass $2500\mathrm{k}\mathrm{g}$ along a straight horizontal road. The lorry and the trailer are connected by a light rigid tow-bar which is parallel to the road.

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• Question 4May/June 2025, paper 41Structured6 marks

  A lorry of mass $18000\text{ kg}$ is travelling along a straight road. On a horizontal section of the road, the power of the lorry’s engine is constant. There is a constant resistance to motion of $1600\text{ N}$.

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