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

Question

A particle moves in a straight line so that its displacement, $s$ metres, from a fixed point $O$ on the straight line is given by $s = -t^3 + 2t^2 + 8t - 6$ for $t \le 3$, where $t$ is the time in seconds after passing through a point $P$ on the line.

Find

The distance $OP$
The distance from $O$ of the particle when it is instantaneously at rest,
The total distance travelled by the particle during the first $3$ seconds
The velocity of the particle when $t = 3$

Accepted Answer

(a) $6\text{ m}$ (b) $\dfrac{-2+112\sqrt7}{27}\text{ m}=10.9\text{ m}$ (c) $\dfrac{-85+224\sqrt7}{27}\text{ m}=18.8\text{ m}$ (d) $-7\text{ m/s}$

Kinematics - Differentiating Displacement and Velocity

Kinematics - Differentiating Displacement and Velocity

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