# Velocity and Acceleration

A particle is moving in positive x-direction with its velocity varying as v= α√x. Assume that at t=0, the particle was located at x=0. Determine the

• the time dependence of velocity
• acceleration
• the mean velocity of the particle averaged over the time that the particle takes to cover the first s metres of the path.

Discussion:

v=α√x.

Squaring both sides

v22x

=2(α2/2)x

Acceleration= α2/2

The initial velocity u is therefore zero and the acceleration is constant.

• v=u+at= (α2/2)t
• The acceleration= α2/2
• V=α√s

Average velocity=(0+v)/2=α√s/2