Relativistic Energy
Relativistic Energy: We have seen that there is a requirement of definition of relativistic linear momentum and similarly one can get the expression of relativistic energy. We can make use of Newton's work-energy theorem. The work done, W on a particle of mass m0by an external force ‘F' gives rise to gain in its kinetic energy.
. . . . . . . . . . . . . . . . . . ( 1 )
or 
. . . . . . . . . . . . . . . . . . ( 2 )
Change in kinetic energy 
. . . ( 3 )
By substituting the relativistic expression for 
and by writing 
. . . . . . . . . . ( 4 )
We konw that,
or 
. . . . . . . . . . . . . . . . . . . . . . . . . . ( 5 )
So, eqn. (4) can be written as,
. . . . . . . . . . . . . ( 6 )
where it is assumed that the particle was at rest initially and its final velocities is V
The second integration in equation (6) can be carried out easily based on substitution method,
say, 
so equation (6) can be written as,
