7. A particle \(P\) moves in a straight line so that its displacement \(s\) metres from a fixed point \(O\) at time \(t\) seconds is given by the formula \(s = t ^ { 3 } - 7 t ^ { 2 } + 8 t\).
- Find the values of \(t\) when the velocity of \(P\) equals zero, and briefly describe what is happening to \(P\) at these times.
- Find the distance travelled by \(P\) between the times \(t = 3\) and \(t = 5\).
- Find the value of \(t\) when the acceleration of \(P\) is \(- 2 \mathrm {~ms} ^ { - 2 }\). Briefly explain the significance of a negative acceleration at this time.