Recently I have been troubled by several things which have been stated in my school physics classes, mainly concerning the classical kinetic energy formula and other formulae derived from it (as well as the 'Work Energy Theorem'). The classical formula for kinetic energy '(mv^2)/2' was first found by two lone french scientists in the early 18th century, with neither proof nor definitive experimental evidence for the key to this formula - the v squared coefficient. If one looks up the proof for this formula, there are several proofs to choose from. The problem with them all is that they utilise the 'Work Energy Theorem', which in itself uses the Kinetic Energy formula in its proof - it doesn't take much to realise something is wrong. Consider this. In a friction-less environment, away from any gravitational influence, there is a rocket. It has an engine with an unlimited fuel supply (to keep mass the same) that is burning at a constant rate. Its rate of fuel consumption is constant (the chemical energy contained within it is being used at a constant rate), and therefore the engine is providing a constant force. This is where I am most likely to wrong in my deduction (if I am). Therefore the energy transformed from chemical energy to kinetic energy can be said to be proportional to the force provided by the engine multiplied by the time it is running. Most importantly, neither the rate of fuel nor the force provided by the engine will change depending on how fast the rocket is moving. From this I get the formula: E (transformed)=f*t Two other formulae which are well known and I assume are accurate: F=ma v=at Simple algebraic manipulation will find that E=mat, and therefore E=mv Mass*velocity, as we all know, is the formula for momentum, NOT kinetic energy. But what exactly is the difference? Why should kinetic energy be proportional to velocity squared and not just velocity. It just doesn't make any sense to me. Isaac newton thought the same, that the 'quantity of motion ' should be mv and not (mv^2)/2, and after all, momentum is conserved in all collisions, not kinetic energy, so surely the definitions should be reversed at least. Anyway, I would like someone to tell me exactly where I have gone wrong in these deductions (if I have that is). If I have gone wrong, then I will at least understand why, and if I haven't, then why exactly has no one else noticed this?