Mechanics (for Paper 4): past paper questions

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• Question 1May/June 2026, paper 41Structured6 marksHas a diagram

  Coplanar forces of magnitudes $55\text{ N}$, $23\text{ N}$, $20\text{ N}$ and $16\text{ N}$ act at a point in the directions shown in the diagram. Find the magnitude and direction of the resultant force.

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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 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 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 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 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 2Oct/Nov 2023, paper 41Structured5 marksHas a diagram

  A particle of mass $2.4\text{ kg}$ is held in equilibrium by two light inextensible strings, one of which is attached to point $A$ and the other attached to point $B$. The strings make angles of ${35}^{\circ }$ and ${40}^{\circ }$ with the horizontal (see diagram).

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• Question 3May/June 2026, paper 41Structured8 marks

  A particle $P$ travels in a straight line, starting from a point $O$. At time $t$ seconds the displacement of $P$ from $O$ is $s$ metres, where $s=4t^3-39t^2+120t$. Find the values of $t$ for which $P$ is instantaneously at rest.

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• Question 3Oct/Nov 2025, paper 41Structured6 marksHas a diagram

  Coplanar forces of magnitudes $45\text{ N}$, $28\text{ N}$, $72\text{ N}$ and $35\text{ N}$ act at a point in the directions shown in the diagram. Find, in either order, the magnitude and direction of the resultant force.

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• Question 3Oct/Nov 2024, paper 41Structured4 marksHas a diagram

  Coplanar forces of magnitudes $52\text{ N}$, $39\text{ N}$ and $P\text{ N}$ act at a point in the directions shown in the diagram. The system is in equilibrium. Find the values of $P$ and $\theta$.

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• Question 3Oct/Nov 2023, paper 41Structured8 marksHas a diagram

  The diagram shows the velocity-time graph for the motion of a bus. The bus starts from rest and accelerates uniformly for $8\text{ seconds}$ until it reaches a speed of $12.6{\text{ m s}}^{-1}$. The bus maintains this speed for $40\text{ seconds}$.

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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 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 4Oct/Nov 2024, paper 41Structured6 marks

  A bus travels between two stops, $A$ and $B$. The bus starts from rest at $A$ and accelerates at a constant rate of $a{\text{ ms}}^{-2}$ until it reaches a speed of $16{\text{ ms}}^{-1}$.

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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 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 5Oct/Nov 2025, paper 41Structured6 marksHas a diagram

  A particle $P$ of mass $m\text{ kg}$ is in equilibrium on a rough plane inclined at an angle ${\theta }^{\circ }$ to the horizontal. The equilibrium of $P$ is maintained by a force of magnitude $8mg\text{ N}$ making an angle ${\theta }^{\circ }$ with a line of greatest slope (see diagram).

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• Question 5Oct/Nov 2024, paper 41Structured10 marks

  A particle, $A$, is projected vertically upwards from a point $O$ with a speed of $80{\text{ ms}}^{-1}$. One second later a second particle, $B$, with the same mass as $A$, is projected vertically upwards from $O$ with a speed of $100{\text{ ms}}^{-1}$.

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• Question 5Oct/Nov 2023, paper 41Structured7 marksHas a diagram

  The diagram shows a particle $A$, of mass $1.2\text{ kg}$, which lies on a plane inclined at an angle of ${40}^{\circ }$ to the horizontal and a particle $B$, of mass $1.6\text{ kg}$, which lies on a plane inclined at an angle of ${50}^{\circ }$ to the horizontal.

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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 6Oct/Nov 2025, paper 41Structured6 marks

  A particle $A$ of mass $2.5\text{ kg}$ is released from rest from the top of a smooth plane, which makes an angle of ${\sin }^{-1}0.2$ with the horizontal.

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• Question 6Oct/Nov 2024, paper 41Structured6 marksHas a diagram

  A particle of mass $1.2\text{ kg}$ is placed on a rough plane which is inclined at an angle $\theta$ to the horizontal, where $\sin \theta =\frac{7}{25}$.

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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 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 7Oct/Nov 2025, paper 41Structured9 marks

  A particle $P$ starts from a point $O$ and moves in a straight line. The velocity $v{\text{ ms}}^{-1}$ of $P$, at time $t\text{ s}$ after leaving $O$, is given by $v=\frac{1}{3}(2t-3)(t-4)$. Find the acceleration of $P$ when $t=2$.

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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 7Oct/Nov 2023, paper 41Structured9 marks

  A particle moves in a straight line starting from a point $O$ before coming to instantaneous rest at a point $X$.

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• Question 2May/June 2026, paper 42Structured4 marks

  Two particles, $A$ and $B$, of masses $2.5\text{ kg}$ and $3.5\text{ kg}$ respectively are at rest on a straight smooth horizontal track. Particle $B$ is situated $9\text{ m}$ from a vertical wall which is fixed at right angles to the track.

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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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