4 A cyclist starts from rest at a point \(A\) and travels along a straight road \(A B\), coming to rest at \(B\). The displacement of the cyclist from \(A\) at time \(t \mathrm {~s}\) after the start is \(s \mathrm {~m}\), where $$s = 0.004 \left( 75 t ^ { 2 } - t ^ { 3 } \right)$$

1. Show that the distance \(A B\) is 250 m .
2. Find the maximum velocity of the cyclist.