I'm looking into studying physics after my affair with comp-sci, but for the time being I have one small issue in particular which has some simple resolution I'm overlooking. In Newtonian physics, the kinetic energy of a particle, if I understand correctly is the square of it's velocity, but my understanding about acceleration is that applying a fixed force to a particle causes fixed acceleration regardless of velocity. So if a force is applied to give it an acceleration of 10 units per second, after 1 second of applying that force, the particle will have a speed of 10 units per second. If the force is applied for twice as long (2 seconds), it would seem to indicate that twice as much energy was input into that particle, and if that particle was accelerating for 2 seconds at 10 units per second, after 2 seconds it's velocity would be 20 units per second. However the square law now suggests that this particle traveling at 20 units per second has FOUR times the energy of the particle traveling at 10 units per second, even though as far as I can tell only twice the energy was put into it. What's the silly thing I am missing here? Thanks.