I'm still learning Calculus at the moment and I'm currently on integration. The moment I realized the "$1/2$" and square value in $v^2$ are just products of integration, can't one just use integrated $v$, assume $m$ is a constant, and hence say $KE$ is really just mass multiplied by its position? e.g. $KE = m * (x + C)$?
I know something's not right, after all $KE$ is the energy of a moving mass, but I'd like to know of other reasons why this won't work too.