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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.

Which of the following is the equation KE = (1/2)mv^2 solved for v?

Learn how to solve the kinetic energy equation KE = (1/2)mv^2 for velocity. This step-by-step solution covers key concepts in algebra and kinematics, providing insight into energy equations. Ideal for high school students in Grades 9-12.

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