A particle starts from rest from a point O and moves in a straight line. The acceleration of the particle at time t after leaving O is a m s^-2, where a = kt^{1/2} for 0 \leq t \leq 9 and where k is a constant. The velocity of the particle at t = 9 is 1.8 m s^-1.

1. Show that k = 0.1.
2. For t > 9, the velocity v m s^-1 of the particle is given by v = 0.2(t - 9)^2 + 1.8.
3. Show that the distance travelled in the first 9 seconds is one tenth of the distance travelled between t = 9 and t = 18.
4. Find the greatest acceleration of the particle during the first 10 seconds of its motion.