5 A particle moves in a straight line starting from a point \(O\). The velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) of the particle \(t \mathrm {~s}\) after leaving \(O\) is given by $$\mathrm { v } = \mathrm { t } ^ { 3 } - \frac { 9 } { 2 } \mathrm { t } ^ { 2 } + 1 \text { for } 0 \leqslant t \leqslant 4$$ You may assume that the velocity of the particle is positive for \(t < \frac { 1 } { 2 }\), is zero at \(t = \frac { 1 } { 2 }\) and is negative for \(t > \frac { 1 } { 2 }\).

1. Find the distance travelled between \(t = 0\) and \(t = \frac { 1 } { 2 }\).
2. Find the positive value of \(t\) at which the acceleration is zero. Hence find the total distance travelled between \(t = 0\) and this instant.