Kinematics - Given the Displacement Function

A particle moves in a straight line so that its displacement, \(s\) meters, from a fixed point \(O\) on the straight line is given by \(s=-t^3+3t^2+9t-5\) for \(t \le 4\), where \(t\) is the time in seconds after passing through a point \(P\) on the line.

1. Find
   1. the distance \(OP\),
   2. the distance from \(O\) of the particle when it is instantaneously at rest,
   3. the total distance travelled by the particle during the first \(4\) seconds,
   4. the velocity of the particle when \(t=4\).
2. At \(t=4\) the acceleration of the particle is changed to \((2t-10)\) \(\mathrm{ms}^{-2}\) the instantaneous velocity remaining unchanged and it finally stops at \(Q\) when \(t=T\). Find the value of \(T\).