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
- the mean velocity of the particle averaged over the time that the particle takes to cover the first s metres of the path.
Squaring both sides
The initial velocity u is therefore zero and the acceleration is constant.
- v=u+at= (α2/2)t
- The acceleration= α2/2