Linear motion under a variable force: past paper questions

Where the questions come from

• Question 3May/June 2026, paper 31Structured9 marks

  A particle $P$ of mass $6.4\text{ kg}$ moves along a straight horizontal line. At time $t\text{ s}$, the speed of $P$ is $v{\text{ ms}}^{-1}$ and the distance of $P$ from its starting position is $x\text{ m}$.

  Try this question
• Question 3Oct/Nov 2025, paper 31Structured7 marks

  A particle $P$ is moving in a straight horizontal line. At time $t\mathrm{s}$, the displacement of $P$ from a fixed point $O$ on the line is $x\mathrm{m}$ and the velocity of $P$ is $v{\mathrm{m}\mathrm{s}}^{-1}$.

  Try this question
• Question 5Oct/Nov 2024, paper 31Structured7 marks

  A particle $P$ of mass $2\mathrm{k}\mathrm{g}$ moving on a horizontal straight line has displacement $x\mathrm{m}$ from a fixed point $O$ on the line and velocity $v\mathrm{m}{\mathrm{s}}^{-1}$ at time $t\mathrm{s}$.

  Try this question
• Question 2Oct/Nov 2023, paper 31Structured7 marks

  A ball of mass $2\text{ kg}$ is projected vertically downwards with speed $5{\text{ ms}}^{-1}$ through a liquid. At time $t\text{ s}$ after projection, the velocity of the ball is $v{\text{ ms}}^{-1}$ and its displacement from its starting point is $x\text{ m}$.

  Try this question
• Question 7Oct/Nov 2025, paper 32Structured10 marks

  A particle $P$ of mass $m\text{ kg}$ moving along a rough horizontal table has displacement $x\text{ m}$ from a fixed point $O$ on the table and velocity $v{\text{ ms}}^{-1}$ at time $t\text{ s}$.

  Try this question
• Question 7Oct/Nov 2024, paper 32Structured11 marks

  A particle $P$ of mass $m\text{ kg}$ is held at rest at a point $O$ and released so that it moves vertically under gravity against a resistive force of magnitude $0.1m{v}^2\text{ N}$, where $v{\text{ ms}}^{-1}$ is the velocity of $P$ at time $t\text{ s}$.

  Try this question
• Question 2May/June 2026, paper 33Structured6 marks

  A particle $P$ of mass $m$ is moving in a straight horizontal line towards a fixed point $A$ on the line. The particle is subject to a resistive force that is inversely proportional to the square of the distance between $P$ and $A$.

  Try this question
• Question 3Oct/Nov 2025, paper 33Structured7 marks

  A particle $P$ is moving in a straight horizontal line. At time $t\mathrm{s}$, the displacement of $P$ from a fixed point $O$ on the line is $x\mathrm{m}$ and the velocity of $P$ is $v\mathrm{m}{\mathrm{s}}^{-1}$.

  Try this question
• Question 6May/June 2023, paper 31Structured9 marks

  A particle $P$ moving in a straight line has displacement $x\mathrm{m}$ from a fixed point $O$ on the line and velocity $v{\mathrm{m}\mathrm{s}}^{-1}$ at time $t\mathrm{s}$. The acceleration of $P$, in ${\mathrm{m}\mathrm{s}}^{-2}$, is given by $6v\sqrt{v+9}$. When $t=0$, $x=2$ and $v=72$.

  Try this question
• Question 1May/June 2025, paper 31Structured5 marks

  A particle $P$ of mass $8\text{ kg}$ is moving in a straight horizontal line. At time $t\text{ s}$, $P$ has displacement $x\text{ m}$ from a fixed point $O$ on the line and velocity $v\text{ m}{\text{s}}^{-1}$.

  Try this question
• Question 6May/June 2024, paper 32Structured9 marks

  A particle $P$ of mass $2\text{kg}$ moving on a horizontal straight line has displacement $x\text{m}$ from a fixed point $O$ on the line and velocity $v{\text{ ms}}^{-1}$ at time $t\text{ s}$.

  Try this question
• Question 6May/June 2023, paper 33Structured10 marks

  A particle of mass $m\text{ kg}$ falls vertically under gravity, from rest. At time $t\text{ s}$, $P$ has fallen $x\text{ m}$ and has velocity $v\text{ m}{\text{ s}}^{-1}$.

  Try this question
• Question 3May/June 2025, paper 33Structured8 marks

  A ball of mass $m\text{ kg}$ is projected vertically upwards with initial speed $U{\text{ ms}}^{-1}$ and moves under gravity. At time $t\text{ s}$ after projection, the ball has travelled a distance $x\text{ m}$ and its speed is $v{\text{ ms}}^{-1}$.

  Try this question
• Question 7May/June 2024, paper 33Structured11 marks

  A parachutist of mass $m\text{ kg}$ opens his parachute when he is moving vertically downwards with a speed of $50{\text{ ms}}^{-1}$.

  Try this question