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Periodic Motion

The equation ...

Question

The equation of motion of a particle moving along a straight line is given by $s = 63 t - 6 t^{2} - t^{3} c m$ .Find its velocity after 2s and the distance covered by it before coming to rest

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Solution

$v = \frac{d s}{d t}$ $s = 63 t - 6 t^{2} - t^{3}$
$v = 63 - 12 t - 3 t^{2}$
at $t = 2$
$v = 27 m / s$
at $t = 0$ $s = 0$
$t = 2$ $s = 63 (2) - 6 (2)^{2} - (2)^{3}$
$= 94 c m$

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