Topic 5.13: Kinematics (HL only) Questions

A lift moves on a vertical line with velocity v(t) = 2t − 3 (m s⁻¹) for 0 ≤ t ≤ 4 s, up positive. (a) Find the acceleration. (b) Find when the lift is instantaneously at rest. (c) Find its displacement from t = 0 to t = 4.

A particle has position s(t) = t³ − 6t² + 9t (metres). Its velocity v(t) is:

A particle has velocity v(t) = t² − 4t (m s⁻¹). Its acceleration a(t) is:

A particle has velocity v(t) m s⁻¹ with v > 0 on 0 ≤ t < 2 and v < 0 on 2 < t ≤ 5. Where does it change direction?

A drone starts from rest on the ground and rises with acceleration a(t) = 12 − 6t (m s⁻²) for 0 ≤ t ≤ 2 s, with v(0) = 0 and s(0) = 0. (a) Find v(t). (b) Find its height s(t), and its height at t = 2 s.

A probe on a straight track has acceleration a(t) = 4 − 2t (m s⁻²), with velocity 1 m s⁻¹ at t = 0. (a) Find the velocity v(t). (b) Find the maximum velocity and the time at which it occurs.

Over 0 ≤ t ≤ 6, a particle's displacement is 0 but its velocity is not always 0. The total distance travelled is:

A particle has acceleration a(t) = 6t (m s⁻²) and is at rest at t = 0. Its velocity v(t) is:

A cyclist rides along a straight path with velocity v(t) = 0.5t² − 4t + 6 (m s⁻¹) for 0 ≤ t ≤ 6 s. (a) Find the times when the cyclist is at rest. (b) Find the displacement and the total distance travelled, and comment on the result.

A particle moves in a straight line with velocity v(t) = 3t² − 12t + 9 (m s⁻¹) for 0 ≤ t ≤ 4 s. Find the total distance travelled.

A small probe moves along a straight rail with velocity v(t) = t² − 5t + 6 (m s⁻¹) for 0 ≤ t ≤ 4 s. Find the total distance travelled.