Question

which formula gives the velocity of the car in simplest form?
$v = \frac{\sqrt{2k}}{m}$
$v = \frac{\sqrt{2km}}{m}$
$v = \frac{\sqrt{2km}}{2m}$

Explanation:

Step1: Start with kinetic energy formula

The kinetic energy formula is $k = \frac{1}{2}mv^2$, where $k$ is kinetic energy, $m$ is mass, $v$ is velocity.

Step2: Isolate $v^2$

Multiply both sides by 2: $2k = mv^2$, then divide by $m$: $v^2 = \frac{2k}{m}$

Step3: Solve for $v$

Take square root of both sides: $v = \sqrt{\frac{2k}{m}}$

Step4: Rationalize the denominator

Rewrite the square root: $v = \frac{\sqrt{2k}}{\sqrt{m}} = \frac{\sqrt{2k} \cdot \sqrt{m}}{\sqrt{m} \cdot \sqrt{m}} = \frac{\sqrt{2km}}{m}$

Answer:

$v = \frac{\sqrt{2km}}{m}$