A particle moving in a straight line starts from rest at a point A and comes instantaneously to rest at a point B. The acceleration of the particle at time t s after leaving A is a m s⁻², where a = 6t^(1/2) – 2t.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [M1] v = ∫ (6t^(1/2) - 2t) dt For integration. v=at is M0.
2. [A1] v = 4t^(3/2) - t² (+c) Allow unsimplified coefficients.
3. [A1] v = 0 leading to t = 0 or t² = 4 leading to t = 16
4. [M1] 6t^(1/2) - 2t = 0 Attempt to solve a = 0, using valid algebra, reaching t = ...
5. [A1] t = 9
6. [M1] s = ∫ (4t^(3/2) - t²) dt For integration of their expression for v which includes a term with a fractional power. Allow unsimplified coefficients. v=at is M0
7. [A1] s = 8/5 t^(5/2) - 1/3 t³ (+c) For correct integral
8. [B1] Distance = 145.8 m Allow 729/5 or 146 to 3s.f.