Momentum: past paper questions

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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 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 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 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 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 5Oct/Nov 2024, paper 42Structured9 marks

  Two particles, $P$ and $Q$, of masses $2m\mathrm{k}\mathrm{g}$ and $m\mathrm{k}\mathrm{g}$ respectively, are held at rest in the same vertical line. The heights of $P$ and $Q$ above horizontal ground are $1\mathrm{m}$ and $2\mathrm{m}$ respectively.

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• Question 5Oct/Nov 2023, paper 42Structured8 marks

  A particle $A$ of mass $0.5\text{ kg}$ is projected vertically upwards from horizontal ground with speed $25\text{ m}{\text{ s}}^{-1}$. Find the speed of $A$ when it reaches a height of $20\text{ m}$ above the ground.

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• Question 7May/June 2026, paper 43Structured13 marksHas a diagram

  Particles $P$ and $Q$ have masses $2\mathrm{k}\mathrm{g}$ and $5\mathrm{k}\mathrm{g}$ respectively. The particles are initially held at rest $3\mathrm{m}$ apart on the same line of greatest slope of a rough plane.

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• Question 4Oct/Nov 2025, paper 42Structured9 marks

  A particle $P$ of mass $0.1\text{ kg}$ is projected vertically upwards with speed $30\text{ m}{\text{ s}}^{-1}$ from horizontal ground.

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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 6Oct/Nov 2025, paper 43Structured7 marks

  Particle $P$ of mass $m\text{ kg}$ and particle $Q$ of mass $2\text{ kg}$ are free to move on a smooth horizontal plane. $P$ and $Q$ are moving directly towards each other with speeds $u{\text{ ms}}^{-1}$ and $3u{\text{ ms}}^{-1}$ respectively.

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• Question 7May/June 2024, paper 41Structured10 marks

  A particle $P$ of mass $0.2\text{ kg}$ is projected vertically upwards from horizontal ground with speed $25{\text{ ms}}^{-1}$. Show that the speed of $P$ when it reaches $20\text{ m}$ above the ground is $15{\text{ ms}}^{-1}$.

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• Question 1May/June 2023, paper 41Structured4 marks

  Two particles $P$ and $Q$, of masses $m\text{ kg}$ and $0.3\text{ kg}$ respectively, are at rest on a smooth horizontal plane. $P$ is projected at a speed of $5{\text{ m s}}^{-1}$ directly towards $Q$.

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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 6May/June 2024, paper 42Structured11 marks

  Three particles $A$, $B$ and $C$ of masses $5\text{ kg}$, $1\text{ kg}$ and $2\text{ kg}$ respectively lie at rest in that order on a straight smooth horizontal track $XYZ$. Initially $A$ is at $X$, $B$ is at $Y$ and $C$ is at $Z$.

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• Question 2May/June 2023, paper 42Structured4 marks

  Two particles $A$ and $B$, of masses $3.2\text{ kg}$ and $2.4\text{ kg}$ respectively, lie on a smooth horizontal table. $A$ moves towards $B$ with a speed of $v\text{ m}{\text{ s}}^{-1}$ and collides with $B$, which is moving towards $A$ with a speed of $6\text{ m}{\text{ s}}^{-1}$.

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• Question 2May/June 2025, paper 42Structured4 marks

  Two particles $P$ and $Q$, of masses $0.2\text{ kg}$ and $0.1\text{ kg}$ respectively, are free to move in a straight line on a smooth horizontal plane. $P$ is projected towards $Q$ with speed $5{\text{ ms}}^{-1}$.

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• Question 1May/June 2024, paper 43Structured3 marks

  Two particles $P$ and $Q$ of masses $0.2\text{ kg}$ and $0.5\text{ kg}$ respectively are at rest on a smooth horizontal plane. Particle $P$ is projected with a speed $6\text{ m}{\text{ s}}^{-1}$ directly towards $Q$.

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• Question 1May/June 2023, paper 43Structured3 marks

  Two particles $P$ and $Q$, of masses $0.1\text{ kg}$ and $0.4\text{ kg}$ respectively, are free to move on a smooth horizontal plane. Particle $P$ is projected with speed $4{\text{ m s}}^{-1}$ towards $Q$ which is stationary.

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• Question 1May/June 2025, paper 43Structured5 marks

  Two particles $P$ and $Q$, of masses $0.1\text{ kg}$ and $0.3\text{ kg}$ respectively, are at rest on a smooth horizontal plane. $P$ is projected directly towards $Q$ with speed $4u{\text{ ms}}^{-1}$.

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