OCR MEI M1 — Question 6

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
TopicNon-constant acceleration

6 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]{34e4ce80-21b0-48f5-865c-de4dd837f7c5-5_624_886_549_631} \captionsetup{labelformat=empty} \caption{Fig. 7}
\end{figure}
  1. Write down the velocity of the insect when \(t = 0\).
  2. Show that the insect is instantaneously at rest when \(t = - 2\) and when \(t = 4\).
  3. Determine the velocity of the insect when its acceleration is zero. Write down the coordinates of the point A shown in Fig. 7.
  4. Calculate the distance travelled by the insect from \(t = 1\) to \(t = 4\).
  5. Write down the distance travelled by the insect in the time interval \(- 2 \leqslant t \leqslant 4\).
  6. How far does the insect walk in the time interval \(1 \leqslant t \leqslant 5\) ?