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CAIE A Level Mathematics 9709

Kinematics of motion in a straight line questions

Exam-style questions on Kinematics of motion in a straight line, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 2 marksFoundationA particle moves in a straight line with constant acceleration. Its initial velocity is 6 m/s, its acceleration is 1 m/s^2, and it moves for 1 seconds. Find its final velocity.
  2. 3 marksFoundationA particle moves in a straight line with initial velocity 2 m/s and constant acceleration 2 m/s^2.
  3. 3 marksFoundationA particle moves in a straight line with initial velocity 3 m/s and constant acceleration 2 m/s². Find the displacement after 5 seconds.
  4. 4 marksStandardA car starts from rest and accelerates uniformly for 6 s until it reaches a speed of 15 m/s. It then travels at this constant speed for 20 s before decelerating uniformly to rest in 2 s. Sketch the velocity–time graph…
  5. 3 marksStandardThe displacement s (in metres) of a particle moving in a straight line is given by s(t) = 3t^2 + 2t, where t is the time in seconds. Find the velocity of the particle at t = 2 seconds.
  6. 4 marksStandardA train starts from rest and accelerates uniformly for 2 seconds, reaching a speed of 6 m/s. It then travels at constant speed for 8 seconds, before decelerating uniformly to rest over a period of 2 seconds. The motion…
  7. 3 marksStandardA vehicle decelerates uniformly from 30 m/s to rest at a constant deceleration of 2 m/s^2. Find the stopping distance, in metres.
  8. 3 marksChallengeA particle moves along a straight line. Its velocity v (in m/s) at time t seconds is given by v = 3t^2 + 2t + 2. Given that the displacement s = 0 when t = 0, find an expression for s in terms of t.
  9. 4 marksChallengeThe acceleration of a particle moving in a straight line is given by a = 2t - 2 m/s^2, where t is the time in seconds. Given that the initial velocity is u = 1 m/s, find the velocity when t = 5 s.
  10. 3 marksChallengeA particle moves in a straight line. Its velocity at time t seconds is given by v(t) = 6t^2 + 4t + 2 m/s. At t=0, the displacement s = 0. Find an expression for s(t) in terms of t.