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.