- A particle \(P\) moves on the \(x\)-axis. At time \(t\) seconds the velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the direction of \(x\) increasing, where \(v\) is given by
$$v = \left\{ \begin{array} { l c }
8 t - \frac { 3 } { 2 } t ^ { 2 } , & 0 \leqslant t \leqslant 4 ,
16 - 2 t , & t > 4 .
\end{array} \right.$$
When \(t = 0 , P\) is at the origin \(O\).
Find
- the greatest speed of \(P\) in the interval \(0 \leqslant t \leqslant 4\),
- the distance of \(P\) from \(O\) when \(t = 4\),
- the time at which \(P\) is instantaneously at rest for \(t > 4\),
- the total distance travelled by \(P\) in the first 10 s of its motion.