Kinematics — AS & A Level Mathematics (9709) questions by topic
Finding when a particle changes direction from an acceleration expression, working out an unknown constant in a velocity-time function given an initial condition, and locating the moment a car's acceleration reaches zero from a cubic velocity function are typical of the 33 kinematics questions from 2023 to 2025, worth between 3 and 13 marks.
Find, show and sketch are the only command words tracked here, each demanding calculus applied to displacement, velocity and acceleration rather than a mechanics diagram of forces. Because integrating or differentiating the wrong kinematic quantity derails a whole answer, submit your working for instant marking to catch a swapped velocity-acceleration relationship at the exact line it occurs.
May–June 2025, Paper 41
The diagram shows the velocity-time graph of the motion of a cyclist. The graph consists of three straight line segments. The cyclist passes a point O with speed 3 m s^-1 and then…
Answer this question and get it marked →A particle X moves along a straight track, starting from a point O at time t = 0. The displacement of X from O at time t s is s m, where s = 3t^(3/2) − 6t. Find the time at which…
Answer this question and get it marked →May–June 2025, Paper 42
A car is travelling along a straight horizontal road. The car passes through a point A, on the road travelling at a speed of 15 m s^-1, and then accelerates uniformly at 0.4 m…
Answer this question and get it marked →A particle P moves in a straight line and passes through the point A at time t = 0. The velocity v m s^-1 of P at time t seconds is given by v = (2t + 1)^(3/2) − 2t^2, where 0 ≤ t…
Answer this question and get it marked →May–June 2025, Paper 43
The diagram shows a velocity-time graph which models the motion of a particle. The graph consists of 3 straight line segments. The vertical axis is v (m s^-1) and the horizontal…
Answer this question and get it marked →A particle X moves in a straight line. The displacement of X from O at time t s after leaving O is s m, where s = 0.3t^2 + 0.6t for 0 <= t <= 4. Find the velocity of X at t = 4.…
Answer this question and get it marked →May–June 2025, Paper 45
A train travels 4.8 km between two stations, A and B. The train starts from rest at A and accelerates at a constant rate until it reaches a speed of 30 m s^-1. It then travels at…
Answer this question and get it marked →A particle P moves in a straight line starting from a point O. At time t s after leaving O, the velocity, v m s^-1, of P is given by v = (15 - 2t)^2. Find the values of t when the…
Answer this question and get it marked →May–June 2024, Paper 41
A car starts from rest and accelerates at 2 m s⁻² for 10 s. It then travels at a constant speed for 30 s. The car then uniformly decelerates to rest over a period of 20 s. Sketch…
Answer this question and get it marked →A particle moves in a straight line, starting from a point O. The velocity of the particle at time t s after leaving O is v m s⁻¹. It is given that v = kt^(1/2) − 2t − 8 (that is,…
Answer this question and get it marked →A particle P of mass 0.2 kg is projected vertically upwards from horizontal ground with speed 25 m s⁻¹. Show that the speed of P when it reaches 20 m above the ground is 15 m s⁻¹.
Answer this question and get it marked →May–June 2024, Paper 42
A particle P moves in a straight line. At time t s after leaving a point O on the line, P has velocity v m s^-1, where v = 44t − 6t^2 − 36. Find the set of values of t for which…
Answer this question and get it marked →May–June 2024, Paper 43
A car travels along a straight road with constant acceleration a m s⁻² (a 0), passing through points A, B and C in that order. Its speed at A is u m s⁻¹ in the direction AB. The…
Answer this question and get it marked →A particle travels in a straight line. Its velocity at time t s after leaving O is v m s⁻¹, where v = kt² − 4t + 3. The distance travelled in the first 2 s is 6 m, and v 0…
Answer this question and get it marked →October–November 2024, Paper 41
A bus travels between two stops, A and B. The bus starts from rest at A and accelerates at a constant rate of a m s^-2 until it reaches a speed of 16 m s^-1. It then travels at…
Answer this question and get it marked →A particle, A, is projected vertically upwards from a point O with a speed of 80 m s^-1. One second later a second particle, B, with the same mass as A, is projected vertically…
Answer this question and get it marked →A particle P moves in a straight line, passing through a point O with velocity 4.2 m s^-1. At time t s after P passes O, the acceleration, a m s^-2, of P is given by a = 0.6t −…
Answer this question and get it marked →October–November 2024, Paper 42
The velocity of a particle moving in a straight line at time t seconds after leaving a fixed point O is v m s⁻¹. The diagram shows a velocity-time graph which models the motion of…
Answer this question and get it marked →Two particles, P and Q, of masses 2m kg and m kg respectively, are held at rest in the same vertical line. The heights of P and Q above horizontal ground are 1 m and 2 m…
Answer this question and get it marked →A particle, P, travels in a straight line, starting from a point O with velocity 6 m s⁻¹. The acceleration of P at time t s after leaving O is a m s⁻², where a = −1.5t^(1/2) for 0…
Answer this question and get it marked →October–November 2024, Paper 43
A particle starts from rest at t = 0 and accelerates at 0.6t m s⁻² for 4 s, reaching a speed of V m s⁻¹. Show that V = 4.8. [1]
Answer this question and get it marked →May–June 2023, Paper 41
A particle P of mass 0.4 kg is projected vertically upwards from horizontal ground with speed 10 m s⁻¹. Find the greatest height above the ground reached by P. [Where a numerical…
Answer this question and get it marked →A particle moves in a straight line starting from rest. The displacement s m of the particle from a fixed point O on the line at time t s is given by s = t^(5/2) − (15/4)t^(3/2) +…
Answer this question and get it marked →The velocity of a particle at time t s after leaving a fixed point O is v m s⁻¹. The diagram shows a velocity–time graph which models the motion of the particle. The graph…
Answer this question and get it marked →May–June 2023, Paper 42
A particle P starts at rest and moves in a straight line from a point O. At time t s after leaving O, the velocity of P, v m s^-1, is given by v = bt + ct^(3/2), where b and c are…
Answer this question and get it marked →May–June 2023, Paper 43
A particle starts from rest at O and moves in a straight line. Its acceleration at time t s is a m s⁻², where a = kt^(1/2) for 0 ≤ t ≤ 9 (k constant). The velocity at t = 9 is 1.8…
Answer this question and get it marked →An elevator is pulled vertically upwards by a cable. It accelerates at 0.4 m s⁻² for 5 s, then travels at constant speed for 25 s, then decelerates at 0.2 m s⁻² until it comes to…
Answer this question and get it marked →October–November 2023, Paper 41
The diagram shows the velocity-time graph for the motion of a bus. The bus starts from rest and accelerates uniformly for 8 seconds until it reaches a speed of 12.6 m s^-1. The…
Answer this question and get it marked →A particle moves in a straight line starting from a point O before coming to instantaneous rest at a point X. At time t s after leaving O, the velocity v m s^-1 of the particle is…
Answer this question and get it marked →October–November 2023, Paper 42
A particle A of mass 0.5 kg is projected vertically upwards from horizontal ground with speed 25 m s⁻¹. Find the speed of A when it reaches a height of 20 m above the ground.
Answer this question and get it marked →A particle X travels in a straight line. The velocity of X at time t s after leaving a fixed point O is denoted by v m s⁻¹, where v = −0.1t³ + 1.8t² − 6t + 5.6. The acceleration…
Answer this question and get it marked →October–November 2023, Paper 43
A particle is projected vertically upwards from horizontal ground with a speed of u m s^-1. The particle has height s m above the ground at times 3 seconds and 4 seconds after…
Answer this question and get it marked →A particle moves in a straight line. At time t s, the acceleration, a m s^-2, of the particle is given by a = 36 - 6t. The velocity of the particle is 27 m s^-1 when t = 2. Find…
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