7 A particle \(P\) moves in a straight line starting from a point \(O\). The velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) of \(P\) at time \(t \mathrm {~s}\) is given by $$\begin{array} { l l } v = 12 t - 4 t ^ { 2 } & \text { for } 0 \leqslant t \leqslant 2 ,
v = 16 - 4 t & \text { for } 2 \leqslant t \leqslant 4 . \end{array}$$

1. Find the maximum velocity of \(P\) during the first 2 s .
2. Determine, with justification, whether there is any instantaneous change in the acceleration of \(P\) when \(t = 2\).
3. Sketch the velocity-time graph for \(0 \leqslant t \leqslant 4\).
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4. Find the distance travelled by \(P\) in the interval \(0 \leqslant t \leqslant 4\).
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