The rest energy of a body of rest mass m_{o}
is m_{o}c^{2} 

If a body is moving relative to an observer
such that its measured mass is m, then its total energy is mc^{2} 

The difference between these two values is
defined to be the kinetic energy of the body (as measured by the
specified observer). 



and putting m in terms of m_{o} and
v, we have 



In general, if x in the expression below is
<< 1 then, to a very good approximation, we can write 



Applying this to our equation for K.E.
above, we obtain 



which simplifies to 



so 



which is the same as the Newtonian
expression for kinetic energy. 



We are thus reminded of the fact that
"relativistic" effects become particularly important when the
relative speeds involved are significant fractions of the speed
of light. 
