Question

the velocity, v, of an object with mass, m, and kinetic energy, e_k, is given by the equation v = √(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 100 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 $v = \sqrt{\frac{2E_{k}}{m}}$. The mass $m = 100$ kg.

Step2: Calculate velocity when $E_{k}=0.6$ J

Substitute $m = 100$ kg and $E_{k}=0.6$ J into the velocity formula $v=\sqrt{\frac{2E_{k}}{m}}$.
$v=\sqrt{\frac{2\times0.6}{100}}=\sqrt{\frac{1.2}{100}}=\sqrt{0.012}\approx0.11$ m/s.

Step3: Calculate kinetic energy when $v = 0.2$ m/s

First, re - arrange the kinetic - energy formula $E_{k}=\frac{1}{2}mv^{2}$. Substitute $m = 100$ kg and $v = 0.2$ m/s into it.
$E_{k}=\frac{1}{2}\times100\times(0.2)^{2}=50\times0.04 = 2$ J.

Step4: Calculate velocity when $E_{k}=8$ J

Substitute $m = 100$ kg and $E_{k}=8$ J into the velocity formula $v=\sqrt{\frac{2E_{k}}{m}}$.
$v=\sqrt{\frac{2\times8}{100}}=\sqrt{\frac{16}{100}} = 0.4$ m/s.

Step5: Calculate kinetic energy when $v = 0$ m/s

Substitute $m = 100$ kg and $v = 0$ m/s into the kinetic - energy formula $E_{k}=\frac{1}{2}mv^{2}$.
$E_{k}=\frac{1}{2}\times100\times0^{2}=0$ J.

Answer:

$E_{k}$ (J)	$v$ (m/s)
2	0.2
8	0.4
0	0