6 A particle \(P\) moves in a straight line. The velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at time \(t \mathrm {~s}\) is given by
$$\begin{array} { l l }
v = 2 t + 1 & \text { for } 0 \leqslant t \leqslant 5 ,
v = 36 - t ^ { 2 } & \text { for } 5 \leqslant t \leqslant 7 ,
v = 2 t - 27 & \text { for } 7 \leqslant t \leqslant 13.5 .
\end{array}$$
- Sketch the velocity-time graph for \(0 \leqslant t \leqslant 13.5\).
- Find the acceleration at the instant when \(t = 6\).
- Find the total distance travelled by \(P\) in the interval \(0 \leqslant t \leqslant 13.5\).
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