7 A vehicle starts from rest at a point \(O\) and moves in a straight line. Its speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at time \(t\) seconds after leaving \(O\) is defined as follows.
$$\begin{aligned}
\text { For } 0 & \leqslant t \leqslant 60 , \quad v = k _ { 1 } t - 0.005 t ^ { 2 }
\text { for } t \geqslant 60 , \quad v & = \frac { k _ { 2 } } { \sqrt { } t }
\end{aligned}$$
The distance travelled by the vehicle during the first 60 s is 540 m .
- Find the value of the constant \(k _ { 1 }\) and show that \(k _ { 2 } = 12 \sqrt { } ( 60 )\).
- Find an expression in terms of \(t\) for the total distance travelled when \(t \geqslant 60\).
- Find the speed of the vehicle when it has travelled a total distance of 1260 m .