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To Calculate Kinetic Energy When v << c
The rest energy of a body of rest mass mo is moc2  
If a body is moving relative to an observer such that its measured mass is m, then its total energy is mc2  
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 mo 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.  
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