Velocity and Acceleration

Let's discuss a beautiful problem from Physics Olympiad based on Velocity and Acceleration.

The Problem: 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

v²=α²x

=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