To find the velocity given the kinetic energy (KE) and mass (m) of an object, we start with the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Here, [tex]\( KE \)[/tex] stands for kinetic energy, [tex]\( m \)[/tex] is mass, and [tex]\( v \)[/tex] is velocity. We need to solve for [tex]\( v \)[/tex]:
1. Begin by isolating [tex]\( v^2 \)[/tex]:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Multiply both sides by 2 to get:
[tex]\[ 2 KE = m v^2 \][/tex]
2. Next, solve for [tex]\( v^2 \)[/tex]:
[tex]\[ v^2 = \frac{2 KE}{m} \][/tex]
3. Finally, take the square root of both sides to solve for [tex]\( v \)[/tex]:
[tex]\[ v = \sqrt{\frac{2 KE}{m}} \][/tex]
Therefore, the correct formula to find the velocity given kinetic energy and mass is:
[tex]\[ v = \sqrt{\frac{2 KE}{m}} \][/tex]
From the given choices, this corresponds to:
[tex]\[ v = \sqrt{\frac{2 KE}{m}} \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
