Energy, work and power: 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 2Oct/Nov 2024, paper 41Structured5 marksHas a diagram

  A particle of mass $7.5\text{ kg}$, starting from rest at $A$, slides down an inclined plane $AB$. The point $B$ is $12.5\text{ metres}$ vertically below the level of $A$, as shown in the diagram.

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• Question 1Oct/Nov 2023, paper 41Structured3 marks

  A particle of mass $1.6\text{ kg}$ is projected with a speed of $20{\text{ m s}}^{-1}$ up a line of greatest slope of a smooth plane inclined at $\alpha$ to the horizontal, where $\tan \alpha =\frac{3}{4}$.

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• Question 6May/June 2026, paper 41Structured10 marks

  Three small smooth spheres $A$, $B$ and $C$ of equal radii and masses $m\text{ kg}$, $2\text{ kg}$ and $4\text{ kg}$ respectively, lie at rest in that order in a straight line on a smooth horizontal plane.

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• Question 2Oct/Nov 2025, paper 41Structured5 marks

  Two particles, $P$ and $Q$, of masses $3\text{ kg}$ and $5\text{ kg}$ respectively, are at rest on a smooth horizontal plane. $P$ is projected at a speed of $4{\text{ ms}}^{-1}$ directly towards $Q$. After $P$ and $Q$ collide, $P$ has speed $1{\text{ ms}}^{-1}$.

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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 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 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 4Oct/Nov 2025, paper 41Structured6 marksHas a diagram

  Two particles, $A$ and $B$, of masses $m\text{ kg}$ and $3\text{ kg}$ respectively, are connected by a light inextensible string. Particle $B$ is on a fixed plane which is at an angle of ${\sin }^{-1}0.6$ to the horizontal ground.

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• Question 2Oct/Nov 2024, paper 42Structured4 marks

  A block of mass $20\mathrm{k}\mathrm{g}$ is held at rest at the top of a plane inclined at ${30}^{\circ }$ to the horizontal. The block is projected with speed $5{\mathrm{m}\mathrm{s}}^{-1}$ down a line of greatest slope of the plane. There is a resistance force acting on the block.

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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 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 3Oct/Nov 2025, paper 42Structured8 marks

  A car of mass $1400\text{ kg}$ travelling on a straight horizontal road accelerates uniformly from a speed of $15\text{ m}{\text{ s}}^{-1}$ to $20\text{ m}{\text{ s}}^{-1}$ over a distance of $175\text{ m}$. Find the time taken to travel the $175\text{ m}$.

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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 1Oct/Nov 2023, paper 42Structured4 marks

  A block of mass $15\text{ kg}$ slides down a line of greatest slope of an inclined plane. The top of the plane is at a vertical height of $1.6\text{ m}$ above the level of the bottom of the plane.

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• Question 4May/June 2026, paper 42Structured9 marksHas a diagram

  A particle $P$ is projected from a point $A$ with speed $4{\text{ ms}}^{-1}$ up a line of greatest slope of a rough plane inclined at an angle $\theta$ to the horizontal, where $\tan \theta =\frac{4}{3}$. $P$ comes to instantaneous rest at a point $B$ on the plane (see diagram).

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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 1Oct/Nov 2024, paper 43Structured4 marks

  An athlete has mass $m\text{ kg}$. The athlete runs along a horizontal road against a constant resistance force of magnitude $24\text{ N}$.

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• Question 3Oct/Nov 2023, paper 42Structured5 marksHas a diagram

  A block of mass $10\text{ kg}$ is at rest on a rough plane inclined at an angle of ${30}^{\circ }$ to the horizontal. A force of $120\text{ N}$ is applied to the block at an angle of ${20}^{\circ }$ above a line of greatest slope (see diagram).

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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 3Oct/Nov 2025, paper 43Structured7 marks

  A block of mass $4\text{ kg}$ is pulled along a rough horizontal road by a constant force of magnitude $25\text{ N}$ acting at an angle of ${36}^{\circ }$ above the horizontal.

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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 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 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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• Question 4Oct/Nov 2024, paper 43Structured6 marksHas a diagram

  Two particles, $A$ and $B$, of masses $3\text{ kg}$ and $6\text{ kg}$ respectively, lie on a smooth horizontal plane. Initially, $B$ is at rest and $A$ is moving towards $B$ with speed $8\text{ m}{\text{s}}^{-1}$.

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• Question 2Oct/Nov 2023, paper 43Structured5 marksHas a diagram

  A machine for driving a nail into a block of wood causes a hammerhead to drop vertically onto the top of a nail. The mass of the hammerhead is $1.2\text{ kg}$ and the mass of the nail is $0.004\text{ kg}$ (see diagram).

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• Question 5May/June 2025, paper 41Structured7 marks

  When a particle $P$ of mass $m\text{ kg}$ has speed $u\text{ m}{\text{s}}^{-1}$, its momentum is $4\text{ N}\text{s}$ and its kinetic energy is $16\text{ J}$. Find the value of $m$ and the value of $u$.

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• Question 3May/June 2024, paper 41Structured4 marks

  A train of mass $180000\text{ kg}$ ascends a straight hill of length $1.5\text{ km}$, inclined at an angle of ${1.5}^{\circ }$ to the horizontal.

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• Question 4Oct/Nov 2023, paper 43Structured7 marks

  A car has mass $1600\text{ kg}$.

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