Example: 1. A force F = ax acts on a particle along positive x axis where a is a constant and x is the displacement of the particle at any instant. Calculate the work done to move the particle by the force along positive x axis from x_{1} to x_{2}.

At any instant the position of the particle is x, therefore force acting on the particle is F = ax.

The work done to displace the particle for dx is dw = . = Fdxcos0^{0} = axdx.

Therefore, the total work done to displace the particle from x_{1} to x_{2} is W = = axdx = .