Energy possessed by a body by virtue of its motion is kinetic energy.

**Derivation:**

Consider a body of mass m initially at rest. If on application of force F, it travels a distance s, then

Work done, W = F x s

By Newton’s second law, F = ma

W = ma x s

where, a = acceleration

Using equation of motion v^{2} - u^{2} =2as, we get

(v^{2}-u^{2})/2 = as

W = m x (v^{2} - u^{2})/2

As intial velocity is zero, W = ½mv^{2}

This work done is stored as kinetic energy of the object.

So, KE = ½ mv^{2}

Let the mass of lighter object be m1 and that of heavier object be m_{2}.

m_{1}< m_{2}

p_{1}= p_{2}

For a given momentum, KE∝ 1/m So

Since

, so lighter object has larger kinetic energy.