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Why is kinetic energy 1/2 mv^2?

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This is probably a stupid question because the answer is likely "it just is".
I am reading Calculus: The elements by Michael Comenetz, and when talking about mQ, he goes on to say "there happens to be advantage in working with 1/2 mQ rather than mQ itself", and then gives the equation k = 1/2 mv^2, but does not explain where the 1/2 came from, he just claims there is an advantage to using it. Is there a reason for this?

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