A particle \(P\), travels in a straight line, so that its displacement, \(s\) m, from \(O\) at time \(t\) seconds, is modelled by \(s=\frac{1}{3}t^3-5t^2-3\).
Find the value of \(t\) when particle \(P\) returns to its initial position.[2]
Find the minimum velocity of particle \(P\).[3]
Another particle, \(Q\), travels in a straight line from \(O\) such that its velocity, \(v\) m/s, at time \(t\) seconds after passing \(O\) is given by \(v=24\left(e^{\frac{t}{6}}-e^{-t}\right)\). Find the value of \(t\) at which the particle \(Q\) is instantaneously at rest.[2]
Find the total distance travelled by particle \(Q\) for the first 9 seconds.[4]