adam12349 t1_j5w4or3 wrote
Simply because that is how it remains conserved.
Lets look at the conservation of momentum first. Its a vector quantity. We define momentum p=m×v that way because that is how it remains conserved. Now not only the direction but the "lenght" of that vector is conserved. We can create a scalar quantity based of of that fact. So just a number and call it kinetic energy.
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