Target Mathematics

3.103: Particle with sine velocity

0606/11/M/J/24 — Question 10 · 9 marks

In this question, distances are in metres and time tt is in seconds. Particle PP is at OO when t=0t = 0. Velocity v=3sin2tv = 3\,\mathrm{sin}\,2t for t0t \geqslant 0.
(a)
Find the exact value of tt for which the velocity is zero for the first time after PP leaves OO.
[2]
(b)
Find an expression, in terms of tt, for the displacement of PP from OO at time tt.
[4]
(c)
Find the distance travelled by PP for 0tπ0 \leqslant t \leqslant \pi.
[3]