7 A particle \(P\) starts to move from a point \(O\) and travels in a straight line. The velocity of \(P\) is \(k \left( 60 t ^ { 2 } - t ^ { 3 } \right) \mathrm { ms } ^ { - 1 }\) at time \(t \mathrm {~s}\) after leaving \(O\), where \(k\) is a constant. The maximum velocity of \(P\) is \(6.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that \(k = 0.0002\).
   \(P\) comes to instantaneous rest at a point \(A\) on the line. Find
2. the distance \(O A\),
3. the magnitude of the acceleration of \(P\) at \(A\),
4. the speed of \(P\) when it subsequently passes through \(O\).