Question

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

	200			$e_k$
5		2	0	$v$

Explanation:

Step1: Recall kinetic - energy formula

The formula for kinetic energy is $E_{k}=\frac{1}{2}mv^{2}$, where $m = 25$ kg.

Step2: Find $E_{k}$ when $v = 5$ m/s

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

Step3: Find $v$ when $E_{k}=200$ J

Set $E_{k}=200$ J and $m = 25$ kg in the formula $E_{k}=\frac{1}{2}mv^{2}$. Then $200=\frac{1}{2}\times25\times v^{2}$. First, simplify the right - hand side: $\frac{1}{2}\times25\times v^{2}=\frac{25v^{2}}{2}$. So, $200=\frac{25v^{2}}{2}$. Cross - multiply to get $400 = 25v^{2}$. Then $v^{2}=\frac{400}{25}=16$, and $v = 4$ m/s.

Step4: Find $E_{k}$ when $v = 2$ m/s

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

Step5: Find $v$ when $E_{k}=0$ J

Set $E_{k}=0$ J and $m = 25$ kg in the formula $E_{k}=\frac{1}{2}mv^{2}$. Then $0=\frac{1}{2}\times25\times v^{2}$, which implies $v = 0$ m/s.

Answer:

$E_{k}$ (J)	312.5	200	50	0