Question

The velocity of a particle moving in the positive direction of the x axis varies as v = α√x, where α 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 * metres of the path.

Answer 1

(a) As the particle is in unidirectional motion it is directed along the x-axis all the time. As at t=0,x=0

(b) Let be the time to cover first m of the path. From the Eq.