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 $O$ in its initial direction of travel 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) $1\text{ s}$ (b) $3\ln\dfrac98+\dfrac13\text{ m}\approx0.687\text{ m}$ (c) $a=-\dfrac23\text{ m s}^{-2}<0$; velocity is decreasing (shown).

2024 GESS PRELIMS P1 Q12

2024 GESS PRELIMS P1 Q12

Solution:

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