Hi all, I was doing an A-level Mechanics paper the other day and one of the quesitons was to show that, starting with Hookes law T=(lambda)(x)/(l), show that the energy stored in an elastic rope is (lambda)(e^{2})/(2l). This was ok, I just said that energy stored would be equal to the sum of the work done stretching the rope a small distance δx and as δ tended to zero it would be dx. Which could be re-written as integral with limits e and 0 dx. Which leads to the equation for elastic potential energy. After doing this i realised that kinetic energy is in a similar form, i.e power of 2 and has a multiplying factor of 1/2 which leads me to my question, is 1/2mv^{2} the result of an integral? Has it also got something to do with work done? but with respect to v? Any help would be greatly appreciated!