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The equation given is \( KE = \frac{1}{2}mv^2 \), and you're asked to solve for \( v \).

### 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:
   \[
   2 \cdot KE = mv^2
   \]
   
3. Divide both sides by \( m \) to isolate \( v^2 \):
   \[
   \frac{2 \cdot KE}{m} = v^2
   \]

4. Finally, take the square root of both sides to solve for \( v \):
   \[
   v = \sqrt{\frac{2 \cdot KE}{m}}
   \]

### Correct Answer: **B**
\[
v = \sqrt{\frac{2KE}{m}}
\]

Let me know if you'd like further details or clarification.

### Relative questions:
1. What happens to \( v \) if the kinetic energy \( KE \) is doubled?
2. How is the velocity \( v \) related to mass \( m \) in this equation?
3. What is the physical meaning of kinetic energy in this equation?
4. Can you derive the same equation starting with the formula for velocity and rearranging for \( KE \)?
5. How would the equation change if it involved potential energy instead of kinetic energy?

**Tip**: Always remember to double-check your algebraic manipulations when isolating variables, especially when dealing with squares and square roots.

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

Explore how to isolate velocity (v) in the kinetic energy equation KE = 1/2 mv^2. This guide provides a step-by-step approach to rearranging the formula and using algebraic principles, suitable for high school physics students.

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