10 In this question, all distances are in metres and time, t, is in seconds. A particle P is at a fixed point O at time t = 0. The velocity, v, of P is given by v = 3 sin 2t for t≥ 0.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [2] M1 for attempt at solution of 3 sin 2t = 0 implied by 90 or π/2 A0 for t = 90
2. [2] A1 t = π/2
3. [4] M1 for k cos 2t, k≠ 6 (-3/2 cos 2t)
4. [4] M1 Dep on attempt to find c using their s (s = 3/2 - 3/2 cos 2t)
5. [4] A1 Must be an expression for s (s = 3/2 - 3/2 cos 2t)
6. [3] M1 dep on their s from (b) unless restarted. Must be in the form of k cos 2t (+c). Condone the use of 0 to π as limits. Limits must be the correct way round and subtracted.
7. [3] M1dep for correct substitution of limits at least once and correct use of symmetry
8. [3] A1 (6)