A particle passes a fixed point $O$ and moves in a straight line such that, $t$ s after leaving

Question

A particle passes a fixed point $O$ and moves in a straight line such that, $t$ s after leaving $O$, its velocity, $\mathrm{v}$ m/s, is given by $\mathrm{v} = \frac{3}{t + 2} - \frac{t + 2}{3}$. The particle reaches its greatest distance from $O$ at $P$. Find the time when the particle reaches $P$.[2] Find the distance travelled by the particle when $t = 2$.[5] Show that the velocity of the particle is decreasing at point $P$.[2]

Accepted Answer

(a) $t = 1$ (b) $0.687$ m (c) $a = -\frac{2}{3} < 0$

2024 GESS PRELIMS P1 Q12

2024 GESS PRELIMS P1 Q12