Sec 4 A-Math Kinematics topical questions

A particle moves along a straight line with displacement s = 2t³ − 5t (metres) after t seconds. Find the velocity and the acceleration when t = 1.

A particle has velocity v = 3t² − 12t + 9. Find the times at which it is at rest.

A particle has acceleration a = 6t and its velocity is 2 m/s when t = 0. Find v in terms of t.

A particle has displacement s = t² − 4t metres. Find its displacement when t = 3, and state what the sign tells you.

A particle moves so that s = t³ − 6t² + 9t. Find the times at which it is at rest, and find its acceleration at each of those times.

A particle has displacement s = t² − 4t for 0 ≤ t ≤ 3. Find the total distance travelled.

A particle has acceleration a = 2t + 1. When t = 0 its velocity is 3 m/s and its displacement is 0. Find the displacement when t = 2, giving your answer correct to 3 significant figures.

A particle moves with displacement s = t³ − 9t² + 24t metres for t ≥ 0. (a) Find the times at which it is at rest. (b) Find its displacement from the start when t = 5. (c) Find the total distance travelled in the first 5 seconds.

A particle has velocity v = t(4 − t) m/s for t ≥ 0. (a) Find the maximum velocity and the time at which it occurs. (b) Show that the particle returns to its starting point at t = 6. (c) Find the total distance travelled in the first 6 seconds, giving your answer correct to 3 significant figures.