2024 IGCSE Additional Mathematics May/June 0606/11 Q10

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 \(v=3\sin2t\) for \(t\geq0\).

1. Find the exact value of \(t\) for which the velocity is zero for the first time after \(P\) leaves \(O\).[2]
2. Find an expression, in terms of \(t\), for the displacement of \(P\) from \(O\) at time \(t\).[4]
3. Find the distance travelled by \(P\) for \(0\leq t\leq\pi\).[3]