which dog has the most kinetic energy?
a. a dog of mass 15 kg running with speed 3 m/s
b. a dog of mass 8 kg running with speed 4 m/s
c. a dog of mass 12 kg running with speed 5 m/s
d. a dog of mass 10 kg running with speed 6 m/s

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Accepted Answer

# Explanation:
## Step1: Calculate kinetic energy for option A
The formula for kinetic energy is $K = \frac{1}{2}mv^{2}$. For option A, $m = 15\space kg$ and $v=3\space m/s$.
$$
\begin{align*}
K_A&=\frac{1}{2}\times15\times3^{2}\
&=\frac{1}{2}\times15\times9\
& = 67.5\space J
\end{align*}
$$
## Step2: Calculate kinetic energy for option B
For option B, $m = 8\space kg$ and $v = 4\space m/s$.
$$
\begin{align*}
K_B&=\frac{1}{2}\times8\times4^{2}\
&=\frac{1}{2}\times8\times16\
&=64\space J
\end{align*}
$$
## Step3: Calculate kinetic energy for option C
For option C, $m = 12\space kg$ and $v = 5\space m/s$.
$$
\begin{align*}
K_C&=\frac{1}{2}\times12\times5^{2}\
&=\frac{1}{2}\times12\times25\
&=150\space J
\end{align*}
$$
## Step4: Calculate kinetic energy for option D
For option D, $m = 10\space kg$ and $v = 6\space m/s$.
$$
\begin{align*}
K_D&=\frac{1}{2}\times10\times6^{2}\
&=\frac{1}{2}\times10\times36\
&=180\space J
\end{align*}
$$

# Answer:
D. A dog of mass 10 kg running with speed 6 m/s

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Explanation:

Step1: Calculate kinetic energy for option A

Step2: Calculate kinetic energy for option B

Step3: Calculate kinetic energy for option C

Step4: Calculate kinetic energy for option D

Answer: