6 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 a velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where \(v = 6 t ^ { 2 } - 30 t + 24\).
- Find the set of values of \(t\) for which the acceleration of the particle is negative.
- Find the distance between the two positions at which \(P\) is at instantaneous rest.
- Find the two positive values of \(t\) at which \(P\) passes through \(O\).