To determine the formula that can be used to find the velocity (v) when the kinetic energy (KE) and mass (m) are known, we start by using the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
We want to solve for velocity [tex]\( v \)[/tex], so we need to rearrange this formula to isolate [tex]\( v \)[/tex]. Let's go through the steps:
1. Start with the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
2. To eliminate the fraction, multiply both sides of the equation by 2:
[tex]\[ 2 \cdot KE = m v^2 \][/tex]
3. Next, isolate [tex]\( v^2 \)[/tex] by dividing both sides of the equation by the mass [tex]\( m \)[/tex]:
[tex]\[ v^2 = \frac{2 \cdot KE}{m} \][/tex]
4. Finally, take the square root of both sides to solve for [tex]\( v \)[/tex]:
[tex]\[ v = \sqrt{\frac{2 \cdot KE}{m}} \][/tex]
So, the formula that can be used to find the velocity when kinetic energy and mass are known is:
[tex]\[ v = \sqrt{\frac{2 \cdot KE}{m}} \][/tex]
Among the given options, the correct formula is:
[tex]\[ v = \sqrt{\frac{2 KE}{m}} \][/tex]
