2026 AHS P2 Q14

A particle, travelling along a straight path, passes a point \(P\) and, \(5\) seconds later, passes a point \(Q\). The velocity, \(v\text{ m/s}\), \(t\) seconds after passing \(P\), is given by

\[v=3t^2-13t+12\]

1. Find the time when the particle is instantaneously at rest.[2]
2. Find the distance travelled from \(P\) to \(Q\).[5]