(Requires calculus)

Prove the relativistic work-energy theorem in one dimension. The force exerted on a particle is given not by F=ma, but F=dp/dt. Using the expression for the relativistic momentum of a particle p=γmv, integrate the force exerted on the particle over the distance it would take to get from speed 0 to a speed v, and show that this is equal to the relativistic formula for the kinetic energy of a particle, K=(γ-1)mc2. Why do we use E=γmc2 rather than K in the principle of conservation of energy? (Compare to the classical case)