The velocity of a particle moving in the positive direction of the x axis varies as `v=alphasqrtx`, where `alpha` 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.

Explanation

To solve the problem step by step, we will break it down into two parts as specified in the question.

### Part (a): Time Dependence of Velocity and Acceleration

1. **Given Equation**: The velocity of the particle is given by:
\[ v = \alpha \sqrt{x} \]
...