The velocity of a particle moving in the positive direction of the x axis varies as v = a √x, where a is a positive constant. Assuming that at the moment t = 0 the particle was located at the point x = 0, find:
(a) The time dependence of the velocity and the acceleration of the particle;
(b) The mean velocity of the particle averaged over the time that the particle takes to cover the first s metres of the path.