Question

the velocity, v, of an object with mass, m, and kinetic energy, ek, is given by the equation v = √(2ek/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.
ek 0 8
v 0.2 0.6

Explanation:

Step1: Recall kinetic - energy formula

The formula for kinetic energy is $E_k=\frac{1}{2}mv^{2}$, and the given formula for velocity is $v = \sqrt{\frac{2E_k}{m}}$, where $m = 100$ kg.

Step2: Calculate velocity when $E_k=0$

Substitute $E_k = 0$ and $m = 100$ kg into $v=\sqrt{\frac{2E_k}{m}}$.
$v=\sqrt{\frac{2\times0}{100}}=0$ m/s

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

Use the formula $E_k=\frac{1}{2}mv^{2}$. Substitute $m = 100$ kg and $v = 0.2$ m/s.
$E_k=\frac{1}{2}\times100\times(0.2)^{2}= \frac{1}{2}\times100\times0.04 = 2$ J

Step4: Calculate velocity when $E_k = 8$ J

Substitute $E_k = 8$ J and $m = 100$ kg into $v=\sqrt{\frac{2E_k}{m}}$.
$v=\sqrt{\frac{2\times8}{100}}=\sqrt{\frac{16}{100}} = 0.4$ m/s

Step5: Calculate kinetic energy when $v=0.6$ m/s

Use the formula $E_k=\frac{1}{2}mv^{2}$. Substitute $m = 100$ kg and $v = 0.6$ m/s.
$E_k=\frac{1}{2}\times100\times(0.6)^{2}=\frac{1}{2}\times100\times0.36 = 18$ J

Answer:

$E_k$ (J)	$v$ (m/s)
2	0.2
8	0.4
18	0.6