To solve the given kinetic energy formula for velocity [tex]\( v \)[/tex], let's go through the steps methodically:
The formula for kinetic energy is:
[tex]\[ E = \frac{1}{2} m v^2 \][/tex]
We need to solve this equation for [tex]\( v \)[/tex].
1. Multiply both sides by 2 to isolate the term involving [tex]\( v \)[/tex]:
[tex]\[ 2E = m v^2 \][/tex]
2. Divide both sides by [tex]\( m \)[/tex] to solve for [tex]\( v^2 \)[/tex]:
[tex]\[ v^2 = \frac{2E}{m} \][/tex]
3. Take the square root of both sides to solve for [tex]\( v \)[/tex]:
[tex]\[ v = \sqrt{\frac{2E}{m}} \][/tex]
So, the correct formula for [tex]\( v \)[/tex] is:
[tex]\[ v = \sqrt{\frac{2E}{m}} \][/tex]
Therefore, the correct answer is:
[tex]\[ v = \sqrt{\frac{2E}{m}} \][/tex]
