**Question**

**Define kinetic energy. Derive an expression for the kinetic energy of an object of mass m in moving with a velocity v. **

**Answer**

Kinetic energy is the energy possessed by an object due to its motion.

The expression for the kinetic energy (KE) of an object of mass m moving with a velocity v is:

KE = {1\over2} × m × v^2

**Derivation**

Kinetic energy (E_{k}) = work done

= Force × displacement

= F×s

= m × a × s

= m × v^2\over 2

[**∵ v ^{2} = u^{2} + 2as and in case initial velocity (u) = 0 ∴ v^{2} = 2as or as v^2\over 2**]

∴ KE = {1\over2} × m × v^2

∴ Kinetic Energy = {1\over2} × mass × velocity^2