Let a constant force F works on a body to displacement of x Since the acceleration is using the equation of kinematics

v² = u² +2ax

Thus, W = ½.m(v² - u²)
The quantity K = 1/2mv² called the kinetic energy of the particle.

Work Done by a Variable Force

The work done by force F(r ), in an infinitesimal displacement ds is

W = F.ds

Work done by a Spring

Let x be the displacement of the free end of the spring from its equilibrium position then, the magnitude of spring force is given by

Fx = -kx

Spring force work done can be calculated for a displacement from xi to xf is given by

Ws = - ?Fs.dx = - ?kx.dx
or Ws = - ½ k(xf² – xi² )