KINETIC ENERGY

From the recoil definition of mass, we saw that the mass of an object increases with speed, becoming very large when the speed of the object approaches the speed of light. The formula for the increase in mass with speed was simply

.........(1)

where m0 is the mass of the particle at rest (the rest mass). When we combine this formula with Einstein's equation E = mc², we get as the equation for the energy of a moving particle

...........(2)

According to Equation (2), when a particle is at rest (v = 0), its energy is given by
E₀ = m₀c² rest energy (3)
This energy m⁰ c² is called the rest energy of the particle. As a particle begins to move, its mass, and therefore its energy, increases. The extra energy that a particle acquires as a result of its motion is called kinetic energy. If mc² is the total energy, then the formula for the particle's kinetic energy is

..........(3)