The way I see it, a constant supply of power, say from the engine in a car to its wheels, will cause it to accelerate at a decreasing rate because the kinetic energy the power supplies is proportional to the velocity squared. That makes sense because going faster will cause the car to encounter greater resistive forces, and it's mathematically consistent (i.e. power = force*velocity or acceleration*mass*velocity, for the power to stay constant, acceleration must reduce as velocity increases) so it's a safe conclusion that constant power does not correspond to constant acceleration. But what if there were no resistive forces, say you have a spacecraft with a traditional chemical rocket motor in a vacuum, the rocket is at full throttle and is combusting x litres of fuel per second producing y joules of energy per second (i.e. constant power), and it has a more or less constant thrust in a vacuum, so the acceleration is constant (I know it would technically increase as the fuel tanks get lighter, but I don't think that's relevant as it is conceivable that a very efficient rocket could make this effect negligible). It seems to me that in this case, a constant acceleration is achieved from a constant power input. Anyone know what would actually happen?