(a) The diagram shows the velocity-time graph for a particle P, travelling in a straight line with velocity vms⁻¹ at a time t seconds. P accelerates at a constant rate for the first 10s of its motion, and then travels at constant velocity, 30ms⁻¹, for another 15s. P then accelerates at a constant rate for a further 10s and reaches a velocity of 60ms⁻¹. P then decelerates at a constant rate and comes to rest when t = 55. [Figure 11.1] (b) A particle Q travels in a straight line such that its velocity, `vms⁻¹`, at time `ts` after passing through a fixed point O is given by `v = 4 cos3t-4`.

1. (a)(i)Find the acceleration when `t = 12`.[1]
2. (a)(ii)Find the acceleration when `t = 50`.[1]
3. (a)(iii)Find the total distance travelled by the particle P.[2]
4. (b)(i)Find the speed of Q when `t = 5π/9`.[2]
5. (b)(ii)Find the smallest positive value of t for which the acceleration of Q is zero.[3]
6. (b)(iii)Find an expression for the displacement of Q from O at time t.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.