2. A car starts from rest at a point \(O\) and moves in a straight line. The car moves with constant acceleration \(4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until it passes the point \(A\) when it is moving with speed \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). It then moves with constant acceleration \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for 6 s until it reaches the point \(B\). Find

1. the speed of the car at \(B\),
2. the distance \(O B\). \section*{3.} \section*{Figure 2} \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{e590030f-0c46-42ab-80b8-3627d3c36908-3_386_970_412_575} \captionsetup{labelformat=empty} \caption{Fig. 2}
   \end{figure} A non-uniform plank of wood \(A B\) has length 6 m and mass 90 kg . The plank is smoothly supported at its two ends \(A\) and \(B\), with \(A\) and \(B\) at the same horizontal level. A woman of mass 60 kg stands on the plank at the point \(C\), where \(A C = 2 \mathrm {~m}\), as shown in Fig. 2. The plank is in equilibrium and the magnitudes of the reactions on the plank at \(A\) and \(B\) are equal. The plank is modelled as a non-uniform rod and the woman as a particle. Find
3. the magnitude of the reaction on the plank at \(B\),
4. the distance of the centre of mass of the plank from \(A\).
5. State briefly how you have used the modelling assumption that
   1. the plank is a rod,
   2. the woman is a particle.