A particle, $P$, travels in a straight line so that at time $t$ seconds, its velocity, $v$ m/s

Question

A particle, $P$, travels in a straight line so that at time $t$ seconds, its velocity, $v$ m/s, is given by $$v = \cos \left(\frac{\pi}{4}t + \frac{\pi}{6} \right).$$ The initial displacement of $P$ from a fixed point $O$ is $\frac{1}{\pi}$ m. Find the initial velocity of $P$, giving your answer in exact value.[1] Find the first two values of $t$ when $P$ comes to instantaneous rest.[3] Find the distance travelled by $P$ in the first $4$ seconds.[4]

Accepted Answer

(a) $\frac{\sqrt{3}}{2}\text{ m s}^{-1}$ (b) $1.33\text{ s},\ 5.33\text{ s}$ (c) $2.55\text{ m}$

2025 SCGS PRELIMS P2 Q7

2025 SCGS PRELIMS P2 Q7

Solution:

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