Which formula can be used to find velocity if kinetic energy and mass are known?

Question

v = The square root of one half times K E and mass.
v = Square Root of StartFraction 2 times m over K E EndFraction.
v = Square Root of K E times m
v = Square Root of StartFraction 2 times K E over m EndFraction.

Answer 1

To find the velocity \( v \) when the kinetic energy (\( KE \)) and mass (\( m \)) are known, you can use the formula for kinetic energy, which is given by:

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

To solve for \( v \), you can rearrange this equation as follows:

1. Multiply both sides by 2: \[ 2KE = mv^2 \]

2. Divide both sides by \( m \): \[ \frac{2KE}{m} = v^2 \]

3. Take the square root of both sides: \[ v = \sqrt{\frac{2KE}{m}} \]

Therefore, the correct formula you can use to find velocity based on kinetic energy and mass is:

\[ v = \sqrt{\frac{2KE}{m}} \]

So, the correct answer among your options is:

v = Square Root of StartFraction 2 times K E over m EndFraction.