6 A particle \(P\) starts from rest at a point \(O\) of a straight line and moves along the line. The displacement of the particle at time \(t \mathrm {~s}\) after leaving \(O\) is \(x \mathrm {~m}\), where
$$x = 0.08 t ^ { 2 } - 0.0002 t ^ { 3 }$$
- Find the value of \(t\) when \(P\) returns to \(O\) and find the speed of \(P\) as it passes through \(O\) on its return.
- For the motion of \(P\) until the instant it returns to \(O\), find
(a) the total distance travelled,
(b) the average speed.