7 A particle \(P\) starts from a point \(O\) and moves along a straight line. \(P\) 's velocity \(t\) s after leaving \(O\) is \(\nu \mathrm { m } \mathrm { s } ^ { - 1 }\), where $$v = 0.16 t ^ { \frac { 3 } { 2 } } - 0.016 t ^ { 2 } .$$ \(P\) comes to rest instantaneously at the point \(A\).

1. Verify that the value of \(t\) when \(P\) is at \(A\) is 100 .
2. Find the maximum speed of \(P\) in the interval \(0 < t < 100\).
3. Find the distance \(O A\).
4. Find the value of \(t\) when \(P\) passes through \(O\) on returning from \(A\).