Question

the velocity, $v$, of an object with mass, $m$, and kinetic energy, $e_{k}$, is given by the equation $v = sqrt{\frac{2e_{k}}{m}}$. velocity is measured in m/s, mass is measured in kg, and kinetic energy is measured in j. complete the table below to show the kinetic energy and velocity of a 25 kg object.

Explanation:

Step1: Recall kinetic - energy formula

The kinetic - energy formula is $E_{k}=\frac{1}{2}mv^{2}$, and the given formula for velocity is $v = \sqrt{\frac{2E_{k}}{m}}$, where $m = 25$ kg.

Step2: Calculate velocity when $E_{k}=200$ J

Substitute $m = 25$ kg and $E_{k}=200$ J into the velocity formula $v=\sqrt{\frac{2E_{k}}{m}}$.
$v=\sqrt{\frac{2\times200}{25}}=\sqrt{\frac{400}{25}}=\sqrt{16}=4$ m/s.

Step3: Calculate kinetic - energy when $v = 2$ m/s

Substitute $m = 25$ kg and $v = 2$ m/s into the kinetic - energy formula $E_{k}=\frac{1}{2}mv^{2}$.
$E_{k}=\frac{1}{2}\times25\times2^{2}=\frac{1}{2}\times25\times4 = 50$ J.

Step4: Calculate velocity when $E_{k}=0$ J

Substitute $m = 25$ kg and $E_{k}=0$ J into the velocity formula $v=\sqrt{\frac{2E_{k}}{m}}$.
$v=\sqrt{\frac{2\times0}{25}} = 0$ m/s.

Step5: Calculate kinetic - energy when $v = 5$ m/s

Substitute $m = 25$ kg and $v = 5$ m/s into the kinetic - energy formula $E_{k}=\frac{1}{2}mv^{2}$.
$E_{k}=\frac{1}{2}\times25\times5^{2}=\frac{1}{2}\times25\times25=\frac{625}{2}=312.5$ J.

Answer:

$v$ (m/s)	$m$ (kg)	$E_{k}$ (J)
2	25	50
0	25	0
5	25	312.5