3 A particle travels in a straight line during the time interval \(0 \leqslant t \leqslant 12\), where \(t\) is the time in seconds. Fig. 1 is the velocity-time graph for the motion. \begin{figure}[h] \end{figure}

1. Calculate the acceleration of the particle in the interval \(0 < t < 6\).
2. Calculate the distance travelled by the particle from \(t = 0\) to \(t = 4\).
3. When \(t = 0\) the particle is at A . Calculate how close the particle gets to A during the interval \(4 \leqslant t \leqslant 12\). In this question take \(\boldsymbol { g }\) as \(\mathbf { 1 0 } \mathrm { m } \mathrm { s } ^ { \mathbf { 2 } }\).
   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]{578555c7-e316-47d3-876a-0b6accce8946-3_596_1004_517_499} \captionsetup{labelformat=empty} \caption{Fig. 6}
   \end{figure} For this model,
4. calculate the distance fallen from \(t = 0\) to \(t = 7\),
5. find the acceleration of the ball from \(t = 2\) to \(t = 6\), specifying the direction,
6. obtain an expression in terms of \(t\) for the downward speed of the ball from \(t = 2\) to \(t = 6\),
7. 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 \(v = - \frac { 3 } { 2 } t ^ { 2 } + \frac { 19 } { 2 } t + 7\).
8. Verify that \(v\) agrees with the values given in Fig. 6 at \(t = 2 , t = 6\) and \(t = 7\).
9. Calculate the distance fallen from \(t = 2\) to \(t = 7\) according to this model.