6 A particle starts from a point \(O\) and moves in a straight line. The velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) of the particle at time \(t \mathrm {~s}\) after leaving \(O\) is given by $$v = k \left( 3 t ^ { 2 } - 2 t ^ { 3 } \right)$$ where \(k\) is a constant.

1. Verify that the particle returns to \(O\) when \(t = 2\).
2. It is given that the acceleration of the particle is \(- 13.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for the positive value of \(t\) at which \(v = 0\). Find \(k\) and hence find the total distance travelled in the first two seconds of motion.