Linear motion under a variable force — AS & A Level Further Mathematics (9231) questions by topic
Variable-force dynamics runs through this topic: finding a particle's velocity or displacement when a horizontal force depends on velocity, deducing how far a parachutist falls once air resistance depends on speed, and finding motion under a force that depends on displacement.
Find and deduce are the two command words across 11 questions from 2023 to 2025 papers, worth from 5 to 11 marks, where choosing between a = v dv/dx and a = dv/dt correctly at the outset decides the whole solution. With no examiner-report extracts logged for this topic, submitting each separated-variables derivation for instant marking is the way to confirm the right form of acceleration was chosen before the rest of the integration is trusted.
May–June 2025, Paper 31
A particle P of mass 8 kg is moving in a straight horizontal line. At time t s, P has displacement x m from a fixed point O on the line and velocity v m s^-1. The only horizontal…
Answer this question and get it marked →May–June 2025, Paper 32
A particle P of mass 8 kg is moving in a straight horizontal line. At time t s, P has displacement x m from a fixed point O on the line and velocity v m s^-1. The only horizontal…
Answer this question and get it marked →May–June 2024, Paper 31
A particle P of mass 2 kg moving on a horizontal straight line has displacement x m from a fixed point O on the line and velocity v m s^-1 at time t s. The only horizontal force…
Answer this question and get it marked →May–June 2024, Paper 32
A particle P of mass 2 kg moving on a horizontal straight line has displacement x m from a fixed point O on the line and velocity v m s^-1 at time t s. The only horizontal force…
Answer this question and get it marked →May–June 2024, Paper 33
A parachutist of mass m kg opens his parachute when he is moving vertically downwards with a speed of 50 m s^-1. At time t s after opening his parachute, he has fallen a distance…
Answer this question and get it marked →October–November 2024, Paper 31
A particle P of mass 2 kg moving on a horizontal straight line has displacement x m from a fixed point O on the line and velocity v m s^-1 at time t s. The only horizontal force…
Answer this question and get it marked →May–June 2023, Paper 31
A particle P moving in a straight line has displacement x m from a fixed point O on the line and velocity v m s^-1 at time t s. The acceleration of P, in m s^-2, is given by…
Answer this question and get it marked →May–June 2023, Paper 32
A particle P moving in a straight line has displacement x m from a fixed point O on the line and velocity v m s^-1 at time t s. The acceleration of P, in m s^-2, is given by…
Answer this question and get it marked →May–June 2023, Paper 33
A particle of mass m kg falls vertically under gravity, from rest. At time t s, P has fallen x m and has velocity v m s^-1. The only forces acting on P are its weight and a…
Answer this question and get it marked →October–November 2023, Paper 31
A ball of mass 2 kg is projected vertically downwards with speed 5 m s^-1 through a liquid. At time t s after projection, the velocity of the ball is v m s^-1 and its displacement…
Answer this question and get it marked →October–November 2023, Paper 32
A particle P of mass 0.5 kg moves in a straight line. At time t s the velocity of P is v m s^-1 and its displacement from a fixed point O on the line is x m. The only forces…
Answer this question and get it marked →Other AS & A Level Further Mathematics topics
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