To solve for v, we are going to first divide by everything on the right so that we get the v term by itself:
[tex] \frac{E}{\frac{1}{2}m}=v^{2} [/tex]
[tex] \frac{2E}{m}=v^{2} [/tex]
Then, to solve for v, we are going to take the square root of both sides:
[tex] \sqrt{\frac{2E}{m}}=v [/tex]
So by some algebraic manipulation, we are able to solve for v, which is: [tex] \sqrt{\frac{2E}{m}} [/tex].
