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When I think of energy, it seems intuitive to me that an object moving has energy; kinetic energy to be specific. But mass X velocity does not give the units of energy, mass X velocity^2 does. Now, considering the equation for kinetic energy:KE = 1/2mv^2I understand (hopefully correctly) that the "1/2" is used to average the initial and final states of something, though I'm not sure exactly what is being averaged. Anyway, this is likely an elementary question to you guys, but what exactly does "v^2" represent, and a related question is, why does "v" alone not define energy (aside from the obvious reason that the units don't add up).