A particle $P$ moves in a straight line so that its displacement, $s$ metres, from a fixed point

Question

A particle $P$ moves in a straight line so that its displacement, $s$ metres, from a fixed point $O$, is given by $s = t^3 - 9t^2 + 24t + 2$, where $t$ is the time taken in seconds after the start of motion. Calculate, the initial velocity and acceleration, the values of $t$ when $P$ is instantaneous at rest, the distance travelled in the first $5$ seconds, the average speed of $P$ during the first $5$ seconds.

Accepted Answer

(a) $v(0)=24\text{ m s}^{-1}$, $a(0)=-18\text{ m s}^{-2}$. (b) $t=2,4$ s. (c) $28$ m. (d) $5.6\text{ m s}^{-1}$.

Kinematics - Distance Travelled and Average Speed

Kinematics - Distance Travelled and Average Speed

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