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The given formula is:

\[
E = \frac{1}{2}mv^2
\]

You are asked to isolate \( m \) (mass) from this equation. Here's the step-by-step manipulation:

1. Start with the original formula:

\[
E = \frac{1}{2}mv^2
\]

2. To remove the fraction, multiply both sides of the equation by 2:

\[
2E = mv^2
\]

3. Finally, to isolate \( m \), divide both sides of the equation by \( v^2 \):

\[
m = \frac{2E}{v^2}
\]

Thus, the formula for \( m \) is:

\[
m = \frac{2E}{v^2}
\]

Would you like more details or have any questions? 

Here are some related questions:

1. How do you isolate \( v \) in the same formula?
2. What is the physical interpretation of \( E \), \( m \), and \( v \) in this equation?
3. How is this formula derived from Newtonian mechanics?
4. How would the formula change if the velocity \( v \) is doubled?
5. What are the SI units for energy \( E \), mass \( m \), and velocity \( v \)?

**Tip:** Always check the units of each variable when manipulating formulas to ensure they are consistent.

Using the equation tool manipulate the formula below to isolate for 'm'. E = 1/2 mv^2

Learn how to manipulate the kinetic energy formula E = 1/2 mv^2 to solve for mass (m). Follow this step-by-step algebraic process, suitable for high school students studying physics and algebra. Understand the concepts of energy, mass, and velocity, and how to rearrange the equation.

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