To solve for u, you want to move everything else except u to the other side. I'd start by getting rid of the 1/2's by multiplying each side of the equation by 2:

2(E) = 2(1/2mv^2 - 1/2mu^2)

2E = mv^2-mu^2

Then, factor an "m" out of the two terms on the left side, so we get

2E = m(v^2-u^2)

Divide each side by m:

(2E)/m = (m(v^2 - u^2))/m

(2E)/m= v^2 - u^2

To get rid of the negative in front of the u^2, add u^2 to each side:

(2E)/m + u^2 = v^2

To get u^2 all alone, subtract (2E)/m from each side

u^2 = v^2 - (2E)/m

To isolate u, take the square root of each side

sqrt (u^2) = sqrt (v^2 -(2E)/m))

u = sqrt (v^2 - (2E)/m))

Apr 29th, 2015

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