Question

1. what is the correct rearrangement of the kinetic energy formula $ke=\frac{1}{2}mv^{2}$ to solve for the velocity $v$? a. $v = sqrt{\frac{2ke}{m}}$ b. $v = 2mke$ c. $v=\frac{ke}{\frac{1}{2}m}$ d. $v=\frac{2m}{ke}$

Explanation:

Step1: Isolate $v^{2}$

Starting with $KE=\frac{1}{2}mv^{2}$, multiply both sides by 2 to get $2KE = mv^{2}$. Then divide both sides by $m$: $v^{2}=\frac{2KE}{m}$.

Step2: Solve for $v$

Take the square - root of both sides. Since we are dealing with a physical quantity (velocity), we consider the positive square - root for the magnitude (assuming we are just looking for the speed here), so $v=\sqrt{\frac{2KE}{m}}$.

Answer:

A. $v = \sqrt{\frac{2KE}{m}}$