2026 GESS P2 Q3

A particle travels in a straight line so that \(t\) seconds after leaving a fixed point \(O\), its velocity, \(v\) m/s, is given by \(v=3\cos2t+4\sin2t\).

1. Find the value of \(t\) when the particle first attains its greatest distance from \(O\).[3]
2. Find the total distance travelled by the particle in the interval \(t=0\) to \(t=4\).[6]