The equation given is the formula for kinetic energy:

$KE = \frac{1}{2} mv^2$

We are asked to solve this equation for $v$ (velocity).

Step-by-step solution:

1. Start with the given equation: $KE = \frac{1}{2} mv^2$
2. Multiply both sides by 2 to eliminate the fraction: $2KE = mv^2$
3. Divide both sides by $m$ to isolate $v^2$: $v^2 = \frac{2KE}{m}$
4. Finally, take the square root of both sides to solve for $v$: $v = \sqrt{\frac{2KE}{m}}$

This matches option B.

Would you like any further clarification?

Here are 5 related questions to think about:

1. What are the units for $KE$, $m$, and $v$ in the SI system?
2. How does the velocity $v$ change if the mass $m$ is doubled?
3. What happens to the kinetic energy if the velocity is tripled?
4. Can you derive the formula for $v$ if the potential energy is considered instead of kinetic energy?
5. How would you modify the equation for $v$ if frictional forces were present?

Tip: Always ensure to isolate the variable step-by-step, carefully handling any squares or square roots.