The energy of a particle with rest mass and velocity *v* is where and *c* is the speed of light. Now, if the velocity is changing
(acceleration), then energy is being consumed at a rate of . So, you see, if acceleration is constant, the rate which you must supply
energy (*P*, power, measured in watts which is Joules/s) is proportional
to . This function increases dramatically as you
approach the speed of light ( ).
This is shown in the graph below.