https://file.aiquickdraw.com/mathbot/file/1726319713700fcvhlwri.jpg

We are given the equation:

\[
k = \frac{1}{2} m V^2
\]

We need to solve for \( V \).

### Step-by-Step Solution:

1. Start with the equation:
   \[
   k = \frac{1}{2} m V^2
   \]

2. Multiply both sides by \( 2 \) to eliminate the fraction:
   \[
   2k = m V^2
   \]

3. Divide both sides by \( m \) to isolate \( V^2 \):
   \[
   V^2 = \frac{2k}{m}
   \]

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

Thus, the velocity \( V \) is:

\[
V = \sqrt{\frac{2k}{m}}
\]

Would you like further details on any steps or additional explanations?

Here are 5 related questions you might find useful:
1. What is the physical meaning of the equation \( k = \frac{1}{2} m V^2 \)?
2. How does the value of \( V \) change if the mass \( m \) increases?
3. Can this formula be used to calculate the kinetic energy of an object? How?
4. How would the equation change if we were solving for \( m \) instead of \( V \)?
5. How is the equation related to the conservation of energy?

**Tip**: When solving for a variable, always aim to isolate the term involving that variable first, using inverse operations like multiplication, division, and square roots.

Learn how to solve for velocity (V) in the equation k = 1/2 m V^2. This problem covers key algebraic concepts, including isolating variables and applying the square root. Suitable for high school 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