7 A racing car is moving in a straight line. The acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\) at time \(t \mathrm {~s}\) after the car starts from rest is given by
$$\begin{array} { l l }
a = 15 t - 3 t ^ { 2 } & \text { for } 0 \leqslant t \leqslant 5
a = - \frac { 625 } { t ^ { 2 } } & \text { for } 5 < t \leqslant k
\end{array}$$
where \(k\) is a constant.
- Find the maximum acceleration of the car in the first five seconds of its motion.
- Find the distance of the car from its starting point when \(t = 5\).
- The car comes to rest when \(t = k\). Find the value of \(k\).