I have a really fundamental problem with understanding relationship between force & power. Please help me with this example: An electrically powered space ship (e.g. 100% efficient ionic engine) is travelling through space. No external forces (like nearby stars) act on it. We turn on the engines which work with constant power: P - i.e. energy intake from the batteries is constant through time. To my intuition the ship should be now accelarating with constant accelaration: A. Then force acting on the ship should also be constant: F=ship_mass*A. It seems then that F should be linearly proportional to P. But of course we know that it isn't, because Power is Energy/time and Energy=Force*Distance=0.5*F*A*time^2. So Power increases with time while Force is constant!!! Is my intuition wrong? If engines work with const Power then Accelaration decreases (in void)? This problem bothers me since I wanted to calculate needed power (in terms of idealistic electrical, 100% efficient propulsion) to keep an object hover in air in earth's gravitational field. Thanks in advance!