A particle $P$ leaves a fixed point $O$ and moves in a straight line so that, $t$ s after leav

Question

A particle $P$ leaves a fixed point $O$ and moves in a straight line so that, $t$ s after leaving point $O$, its velocity $v$ m/s, is given by $v = 3\sin 2t + 2$. Find, when $t = 10$, the velocity of $P$, the displacement of $P$ from $O$. Calculate the value of $t$ when $P$ comes to instantaneous rest for the second time, the total distance it has travelled when $t = \frac{3}{4}\pi$.

Accepted Answer

(a) (i) 4.74 m s^{-1}; (ii) 20.9 m from O. (b) (i) 2.78 s; (ii) 6.77 m.

Kinematics - Motion Conditions, Rest and Direction

Kinematics - Motion Conditions, Rest and Direction

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