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 energy is measured in j. complete the table below to show the kinetic energy and velocity of a 25 kg object.

$e_{k}$	$v$
	2
200
	5

Explanation:

Step1: Recall the kinetic - energy formula

Given $v = \sqrt{\frac{2E_k}{m}}$, we can re - arrange it to find $E_k=\frac{mv^{2}}{2}$ (by squaring both sides and cross - multiplying). Here $m = 25$ kg.

Step2: Find $E_k$ when $v = 0$

Substitute $v = 0$ and $m = 25$ into $E_k=\frac{mv^{2}}{2}$. Then $E_k=\frac{25\times0^{2}}{2}=0$.

Step3: Find $E_k$ when $v = 2$

Substitute $v = 2$ and $m = 25$ into $E_k=\frac{mv^{2}}{2}$. So $E_k=\frac{25\times2^{2}}{2}=\frac{25\times4}{2}=50$.

Step4: Find $v$ when $E_k = 200$

Given $v=\sqrt{\frac{2E_k}{m}}$, substitute $E_k = 200$ and $m = 25$. Then $v=\sqrt{\frac{2\times200}{25}}=\sqrt{16}=4$.

Step5: Find $E_k$ when $v = 5$

Substitute $v = 5$ and $m = 25$ into $E_k=\frac{mv^{2}}{2}$. So $E_k=\frac{25\times5^{2}}{2}=\frac{25\times25}{2}=312.5$.

Answer:

$E_k$	$v$
$50$	$2$
$200$	$4$
$312.5$	$5$