4 A particle starts from rest at a point \(X\) and moves in a straight line until, 60 seconds later, it reaches a point \(Y\). At time \(t \mathrm {~s}\) after leaving \(X\), the acceleration of the particle is
$$\begin{array} { r c c }
0.75 \mathrm {~m} \mathrm {~s} ^ { - 2 } & \text { for } & 0 < t < 4
0 \mathrm {~m} \mathrm {~s} ^ { - 2 } & \text { for } & 4 < t < 54
- 0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 } & \text { for } & 54 < t < 60
\end{array}$$
- Find the velocity of the particle when \(t = 4\) and when \(t = 60\), and sketch the velocity-time graph.
- Find the distance \(X Y\).