The given equation is:

$V_e = \frac{1}{2} m v^2$

We need to solve for $v$.

Step-by-step solution:

1. Isolate $v^2$:
   First, multiply both sides of the equation by 2 to get rid of the fraction: $2 V_e = m v^2$

2. Solve for $v^2$:
   Divide both sides by $m$: $v^2 = \frac{2 V_e}{m}$

3. Take the square root:
   Finally, take the square root of both sides to solve for $v$: $v = \sqrt{\frac{2 V_e}{m}}$

Thus, the solution for $v$ is:

$v = \sqrt{\frac{2 V_e}{m}}$

Do you have any questions or would you like further details?

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Here are 5 related questions to consider:

1. What would happen if $V_e = 0$ in this equation?
2. How can this equation be applied to calculate velocity in real-world scenarios?
3. How does this equation relate to kinetic energy?
4. Can you solve for $m$ in terms of $V_e$ and $v$?
5. What physical quantity does $V_e$ represent?

Tip: When solving for variables under square roots, always consider both the positive and negative roots unless context (like velocity) restricts the solution to positive values.