Question

the velocity, v, of an object with mass, m, and kinetic energy, ek, is given by the equation v = √(2ek/m). the mass of the object is 25 kg. complete the table below to show the kinetic energy and velocity of the object.

v	0	2	blank	5
ek	blank	blank	200	blank

Explanation:

Step1: Recall kinetic - energy formula

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

Step2: When $v = 0$

Substitute $v = 0$ and $m = 25$ into the formula: $E_{k}=\frac{1}{2}\times25\times0^{2}=0$ J.

Step3: When $v = 2$

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

Step4: When $E_{k}=200$

We know $E_{k}=\frac{1}{2}mv^{2}$, so $200=\frac{1}{2}\times25\times v^{2}$. First, simplify the equation: $200=\frac{25v^{2}}{2}$, then $400 = 25v^{2}$, and $v^{2}=\frac{400}{25}=16$, so $v = 4$ m/s.

Step5: When $v = 5$

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

Answer:

$v$	$0$	$2$	$4$	$5$