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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

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

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