A particle $P$ moves in a straight line from a fixed point $O$. Its displacement, $s$ metres,

Question

A particle $P$ moves in a straight line from a fixed point $O$. Its displacement, $s$ metres, from $O$ at time $t$ seconds is given by $s=2t^3-9t^2+12t$, where $t\geq0$. Find the displacement of $P$ when $t=3$.[1] Find the positive values of $t$ for which $P$ is instantaneously at rest.[2] Find the range of values of $t$ for which the acceleration of $P$ is positive.[2]

Accepted Answer

(i) $9\text{ m}$ (ii) $t=1\text{ s},\ 2\text{ s}$ (iii) $t>\dfrac32$

Cubic displacement and acceleration sign

Cubic displacement and acceleration sign

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