2024 IGCSE Additional Mathematics May/June 0606/13 Q9

In this question, all lengths are in metres, and time, \(t\), is in seconds.

A particle \(P\) moves in a straight line such that, \(t\) seconds after leaving a fixed point \(O\), its displacement, \(s\), is given by \(s=4t-4\cos2t+4\).

1. Find the velocity, \(v\), of \(P\) at time \(t\).[2]
2. On the axes, sketch the velocity–time graph for \(P\) for \(0\leq t\leq\pi\), stating the intercepts with the axes in exact form.[5]
3. Find the acceleration of \(P\) at time \(t\).[1]
4. Find the times when the acceleration of \(P\) is zero for \(0\leq t\leq\pi\). Give your answers in terms of \(\pi\).[2]