2026 CCHY P2 Q9

A particle moves along a straight line. Its velocity \(v\) m/s at a time \(t\) seconds is given by \(v=t^3-9t^2+18t\). At \(t=0\), the particle is at the point \(O\).

1. Find the initial acceleration.[1]
2. Find the time(s) when the particle is at instantaneous rest.[2]
3. Find an expression for the displacement \(s\) metres from \(O\) at time \(t\).[3]
4. Find the total distance travelled by the particle during the first 4 seconds.[3]
5. Determine whether the particle is moving in the positive or negative direction when \(t=4\).[1]