5 A particle \(P\) moves in a straight line. It starts at a point \(O\) on the line and at time \(t\) s after leaving \(O\) it has velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where \(v = 4 t ^ { 2 } - 20 t + 21\).
- Find the values of \(t\) for which \(P\) is at instantaneous rest.
- Find the initial acceleration of \(P\).
- Find the minimum velocity of \(P\).
- Find the distance travelled by \(P\) during the time when its velocity is negative.