Why is the 1/2 important in the equation Ek = 1/2mv^2?

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Homework Statement


ok..so we know that Ek is by definition 1/2mv^2.
my question is that since Ek is simply defined to be that much..why does the 1/2 matter..
cant we simply write it as Ek = mv^2?

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The Attempt at a Solution

 
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The '1/2' comes into effect during the derivation of the formula for Ek using the basic definition of work done.
 
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