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.