Specimen Paper SPEC/5/TZ0 P2 Q6

The displacement, in centimetres, of a particle from an origin, \(\mathrm{O}\), at time \(t\) seconds, is given by \(s(t) = t^2\cos{t} + 2t\sin{t}\), \(0 \leq t \leq 5\).

1. Find the maximum distance of the particle from \(\mathrm{O}\).

   [3]

2. Find the acceleration of the particle at the instant it first changes direction.

   [4]