Question

question 3 of 25
a dog with mass 14 kg has a kinetic energy of 135.5 j. what is the speed of the dog?

a. 5.1 m/s
b. 3.2 m/s
c. 4.4 m/s
d. 2.3 m/s

Explanation:

Step1: Recall kinetic - energy formula

The formula for kinetic energy is $K = \frac{1}{2}mv^{2}$, where $K$ is kinetic energy, $m$ is mass, and $v$ is speed. We need to solve for $v$.

Step2: Rearrange the formula for $v$

Starting from $K=\frac{1}{2}mv^{2}$, we first multiply both sides by 2 to get $2K = mv^{2}$. Then divide both sides by $m$: $v^{2}=\frac{2K}{m}$. Taking the square - root of both sides gives $v=\sqrt{\frac{2K}{m}}$.

Step3: Substitute the given values

We are given that $K = 135.5\ J$ and $m = 14\ kg$. Substituting these values into the formula $v=\sqrt{\frac{2K}{m}}$, we have $v=\sqrt{\frac{2\times135.5}{14}}=\sqrt{\frac{271}{14}}\approx\sqrt{19.357}\approx 4.4\ m/s$.

Answer:

C. 4.4 m/s