the formula to determine energy is $e = \\frac{1}{2}mv^{2}$. what is the formula solved for…

the formula to determine energy is $e = \\frac{1}{2}mv^{2}$. what is the formula solved for $v$?\n$v=pm\\sqrt{\\frac{m}{2e}}$\n$v = 2e - m$\n$v=pm\\sqrt{2e - m}$\n$v=pm\\sqrt{\\frac{2e}{m}}$

the formula to determine energy is $e = \\frac{1}{2}mv^{2}$. what is the formula solved for $v$?\n$v=pm\\sqrt{\\frac{m}{2e}}$\n$v = 2e - m$\n$v=pm\\sqrt{2e - m}$\n$v=pm\\sqrt{\\frac{2e}{m}}$

Answer

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. Remember, when taking the square root of both sides of an equation, we have two solutions (positive and negative), so $v = \pm\sqrt{\frac{2E}{m}}$.

Answer:

$v=\pm\sqrt{\frac{2E}{m}}$