3.117: Particle: positions of rest and acceleration

0606/22/M/J/21 — Question 8 · 8 marks

(a)
A particle moves in a straight line so that, tt seconds after passing through a fixed point OO, its velocity is v=3t230t+72ms1v=3t^{2}-30t+72\,\mathrm{ms}^{-1}.
Find the distance between the particle's two positions of instantaneous rest.
[6]
(b)
Find the acceleration of the particle when t=2t=2.
[2]