7 Fig. 7 is a sketch of part of the velocity-time graph for the motion of an insect walking in a straight line. Its velocity, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), at time \(t\) seconds for the time interval \(- 3 \leqslant t \leqslant 5\) is given by
$$v = t ^ { 2 } - 2 t - 8 .$$
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3be85526-3872-42ac-8278-1d4a3cf75ff7-5_646_898_552_587}
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\caption{Fig. 7}
\end{figure}
- Write down the velocity of the insect when \(t = 0\).
- Show that the insect is instantaneously at rest when \(t = - 2\) and when \(t = 4\).
- Determine the velocity of the insect when its acceleration is zero.
Write down the coordinates of the point A shown in Fig. 7.
- Calculate the distance travelled by the insect from \(t = 1\) to \(t = 4\).
- Write down the distance travelled by the insect in the time interval \(- 2 \leqslant t \leqslant 4\).
- How far does the insect walk in the time interval \(1 \leqslant t \leqslant 5\) ?