k=1/2mv^2 solve for v (show work plz)?

Answer 1

You want to bring everything on the right side with the v to the left. First, multiply both sides by 2 (to take care of the 1/2)

2k = mv^2
Divide both sides by m
2k/m = v^2
Take the square root of both sides. Remember there are two possibilites because this involves a square root.

+-(sqrt)(2k/m) = v

If you're required to get rid of the radical in the denominator, then you have to multiply the left side by (sqrt)m/(sqrt)m
+- ((sqrt)2km) / m = v

Answer 2

2 k = m v ²
v ² = 2 k / m
v = √ ( 2k / m )

Answer 3

k=1/2mv^2
times 2
2k=mv^2
(2k)/m=v^2
root
√(2k)/m=v