consider 2 identical rockets, same mass and size, same engine which gives a constant thrust. the rockets are both moving upward. the thrust of the engine is equal to the weight of the rocket (assume the mass of the fuel lost is negligable). therefore the forces are balanced so if one of the rockets is moving at v, it will continue to move at v until it runs out of fuel. consider them at some arbitrary height and set this point as potential energy = 0. now consider the 2 rockets as they both move from this height to some greater height h. let the speed of rocket A be v, and the speed of rocket B be 10v. since the rocket thrust equals the weight, the velocities will remain at v and 10v respectivly. therefore rocket A will take much longer to reach the height h than rocket B. if the engines of both rockets provide the same thrust, the would burn fuel at the same rate. therefore since rocket B reaches height h faster, it will burn less fuel, but gain more potential energy than rocket A. how can this be???? mathmatically the work done by each engine will be the same since the force is the same and the distance is the same. The power would also work out as expected, the power provided by rocket B is greater since it does the same amount of work in less time. however it seems then that rocket b will provide more power will burning less fuel...???? unless rocket B actually burns MORE fuel.....but why should a rocket engine burn more fuel just because it is going faster? think of it like this, you have a large block with a small block attached to it. if you throw the small block away from the large block, accelerating it, you apply a force on it for a certain period of time. the force is also applied over a certian distance relative to the large block. an equal and opposite force acts on the large block for the same amount of time. this is the same regardless of how fast the system is going at the beginning.