6 The speed of a 100 metre runner in \(\mathrm { ms } ^ { - 1 }\) is measured electronically every 4 seconds.
The measurements are plotted as points on the speed-time graph in Fig. 6. The vertical dotted line is drawn through the runner's finishing time.
Fig. 6 also illustrates Model P in which the points are joined by straight lines.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{13f555cc-d506-48e5-a0e4-225cae4251dc-6_1025_1504_641_260}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{figure}
- Use Model P to estimate
(A) the distance the runner has gone at the end of 12 seconds,
(B) how long the runner took to complete 100 m .
A mathematician proposes Model Q in which the runner's speed, \(v \mathrm {~ms} ^ { - 1 }\) at time \(t \mathrm {~s}\), is given by
$$v = \frac { 5 } { 2 } t - \frac { 1 } { 8 } t ^ { 2 }$$ - Verify that Model Q gives the correct speed for \(t = 8\).
- Use Model Q to estimate the distance the runner has gone at the end of 12 seconds.
- The runner was timed at 11.35 seconds for the 100 m .
Which model places the runner closer to the finishing line at this time?
- Find the greatest acceleration of the runner according to each model.