A particle starts from a point O and moves in a straight line. The velocity v m s^-1 of the particle at time t s after leaving O is given by

\(v = k(3t^2 - 2t^3)\),

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 m 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.