2026 MSHS P2 Q10

A particle is travelling in a straight line. Its velocity, \(v\) m/s, where \(t\) is the time in seconds after passing a fixed point \(O\), is given by \(v=3-6\sin3t\).

1. Determine the range of values of \(v\).[1]
2. Find the exact values of \(t\) for the first two times the particle is at instantaneous rest.[3]
3. Find the displacement of the particle when \(t=\dfrac{5\pi}{18}\).[3]
4. Find the distance travelled by the particle for the first \(\dfrac\pi2\) seconds.[2]