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 $s = t^3 - 2t^2 - 12t - 5$, where time $t$ is the time taken in seconds after the start of motion. Calculate the initial velocity and acceleration, the value(s) of $t$ when $P$ is instantaneously at rest, the distance travelled in the first $5$ seconds, the average speed of $P$ during the first $5$ seconds

Accepted Answer

(a) Initial velocity $-12\text{ m s}^{-1}$, initial acceleration $-4\text{ m s}^{-2}$; (b) $t=\dfrac{2+2\sqrt{10}}3\text{ s}$; (c) $\dfrac{869+320\sqrt{10}}{27}\text{ m}$; (d) $\dfrac{869+320\sqrt{10}}{135}\text{ m s}^{-1}$

Kinematics - Differentiating Displacement and Velocity

Kinematics - Differentiating Displacement and Velocity

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