F = m * a, so W = m * a * s

Transferring this to units of measurement gives us: J = kg * m * s

^{-2}* m

Or simplified: J = kg * m

^{2}* s

^{-2}

Transferring back to units of quantity: W = m * v

^{2}

How can that be correct? Obviously E

_{kin}= 1/2 * m * v

^{2}. Where did that 1/2 go? Or is W =/= E

_{kin}? Am I making some other kind of mistake?