https://file.aiquickdraw.com/mathbot/file/1729275126097wg0xanf6.jpg

To isolate \( v \) in the formula for kinetic energy:

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

Here are the steps:

1. **Multiply both sides by 2** to get rid of the fraction:
   \[
   2E = mv^2
   \]

2. **Divide both sides by \( m \)** to isolate \( v^2 \):
   \[
   v^2 = \frac{2E}{m}
   \]

3. **Take the square root of both sides** to solve for \( v \):
   \[
   v = \sqrt{\frac{2E}{m}}
   \]

Thus, the final equation is:
\[
v = \sqrt{\frac{2E}{m}}
\]

Would you like any further details or explanations?

Here are 5 related questions to explore:

1. How does the formula change if you include a potential energy term?
2. What does the variable \( m \) represent, and how does it affect \( v \)?
3. What units would \( E \), \( m \), and \( v \) be in for this equation?
4. How can this formula be applied in the context of classical mechanics?
5. What would the formula look like if you wanted to solve for \( E \) instead of \( v \)?

**Tip:** When dealing with square roots in physics, always consider whether you need both the positive and negative root, especially when dealing with velocities.

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

Learn how to isolate the velocity (v) from the kinetic energy formula E = 1/2 mv^2. This step-by-step guide explains the key algebraic manipulations to solve for 'v' and apply it to physics problems. Suitable for high school physics students (Grades 9-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation