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

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

[∵ v² = u² + 2as and in case initial velocity (u) = 0 ∴ v² = 2as or as v^2\over 2]

∴ KE = {1\over2} × m × v^2

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