Kinetic energy of a particle of mass
m moving at speed
v comparable to the speed of light in vacuum
c is:
When the speed of the particle is much lower than the speed of light, i.e. when:
we can use the generalized binomial formula to expand the square root:
to get the non-relativistic expression for the kinetic energy:
As you can see, the non-relativistic expression for the kinetic energy is only the lowest order term in the expansion of the relativistic expression in powers of the small quantity
v/
c. This approximation breaks down for speed comparable to the speed of light. Indeed, when
you can see that the kinetic energy
. So, the speed of light in relativity plays effectively a role of an infinite speed that cannot be reached.