Question

select the correct answer. the formula for finding the kinetic energy, e, of an object is given below, where m represents the mass and v represents the speed of the object. $e = \frac{1}{2}mv^{2}$ solve the formula for v. $v = sqrt{\frac{2e}{m}}$ $v = sqrt{\frac{m}{2e}}$ $v = \frac{4e^{2}}{m}$ $v = sqrt{\frac{e}{2m}}$

Explanation:

Step1: Isolate $v^{2}$

Multiply both sides of $E=\frac{1}{2}mv^{2}$ by $2$ to get $2E = mv^{2}$, then divide both sides by $m$: $v^{2}=\frac{2E}{m}$.

Step2: Solve for $v$

Take the square - root of both sides. Since $v$ represents speed (a non - negative quantity in the context of kinetic energy formula in basic physics, we consider the principal square root): $v=\sqrt{\frac{2E}{m}}$.

Answer:

$v=\sqrt{\frac{2E}{m}}$ (corresponding to the first option in the multiple - choice list)