5 Fig. 3 is a sketch of the velocity-time graph modelling the velocity of a sprinter at the start of a race.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{34e4ce80-21b0-48f5-865c-de4dd837f7c5-4_581_1085_453_567}
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\caption{Fig. 3}
\end{figure}
- How can you tell from the sketch that the acceleration is not modelled as being constant for \(0 \leqslant t \leqslant 4\) ?
The velocity of the sprinter, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), for the time interval \(0 \leqslant t \leqslant 4\) is modelled by the expression
$$v = 3 t - \frac { 3 } { 8 } t ^ { 2 } .$$
- Find the acceleration that the model predicts for \(t = 4\) and comment on what this suggests about the running of the sprinter.
- Calculate the distance run by the sprinter from \(t = 1\) to \(t = 4\).