Derive the expression for kinetic energy from the work–energy theorem.

 

The work–energy theorem states that the work done on an object is equal to the change in its kinetic energy. Let a force F act on a body of mass m, producing an acceleration a.

From Newton’s 2nd law: F = ma

Work done, W = F × d = ma × d

Using equation of motion: v² – u² = 2ad → ad = (v² – u²)/2

So, W = ma × d = m × (v² – u²)/2

W = ½ mv² – ½ mu²

Thus, the work done equals the change in kinetic energy:

K.E. = ½ mv²

This derivation shows that kinetic energy depends on both mass and velocity. A moving car has greater kinetic energy than a bicycle at the same speed because of its higher mass.