6 In this question take \(g\) as \(10 \mathrm {~m \mathrm {~s} ^ { - 2 }\).}
A small ball is released from rest. It falls for 2 seconds and is then brought to rest over the next 5 seconds. This motion is modelled in the speed-time graph Fig. 6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c84a748a-a6f4-48c5-b864-fe543569bdf5-5_659_1105_578_493}
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\caption{Fig. 6}
\end{figure}
For this model,
- calculate the distance fallen from \(t = 0\) to \(t = 7\),
- find the acceleration of the ball from \(t = 2\) to \(t = 6\), specifying the direction,
- obtain an expression in terms of \(t\) for the downward speed of the ball from \(t = 2\) to \(t = 6\),
- state the assumption that has been made about the resistance to motion from \(t = 0\) to \(t = 2\).
The part of the motion from \(t = 2\) to \(t = 7\) is now modelled by \(v = - \frac { 3 } { 2 } t ^ { 2 } + \frac { 19 } { 2 } t + 7\).
- Verify that \(v\) agrees with the values given in Fig. 6 at \(t = 2 , t = 6\) and \(t = 7\).
- Calculate the distance fallen from \(t = 2\) to \(t = 7\) according to this model.