3.116: Trigonometric velocity; acceleration and displacement

0606/13/M/J/22 — Question 5 · 8 marks

(a)
The velocity v ms−1v\,\mathrm{ms}^{-1} of a particle moving in a straight line, tt seconds after passing through OO, is v=6sin⁡3tv=6\sin 3t.
Find the time at which the acceleration is first equal to −9 ms−2-9\,\mathrm{ms}^{-2}.
[4]
(b)
Find the displacement of the particle from OO when t=5.6t=5.6.
[4]