Answer: C. The kinetic energy of the object is $0$ joules when the object is traveling at a speed of $0$ meters per second.

Explanation:1. Identify the given function: $K(v) = \dfrac{1}{2}(75)(v^2)$, where $K(v)$ is the kinetic energy in joules of an object with mass $75$ kilograms traveling at a speed of $v$ meters per second.

2. Identify the specific value given for interpretation: $K(0) = 0$.

3. Interpret the input and output of the function in the expression $K(0) = 0$: - The input to the function $K$ is $v$, the speed in meters per second. In $K(0)$, the input $v=0$. This means the speed of the object is $0$ meters per second. - The output of the function $K(v)$ is the kinetic energy in joules. In $K(0)=0$, the output is $0$. This means the kinetic energy is $0$ joules.

4. Combine these interpretations: $K(0) = 0$ means that when the speed of the object ($v$) is $0$ meters per second, the kinetic energy of the object ($K(v)$) is $0$ joules.

5. Evaluate the given options: - [A] The kinetic energy of the object is $0$ joules when the mass of the object is $0$ kilograms. (The mass is given as $75$ kilograms and is not the variable in $K(0)$). - [B] The speed of the object is $0$ meters per second when the mass of the object is $0$ kilograms. (This confuses the input and output with mass). - [C] The kinetic energy of the object is $0$ joules when the object is traveling at a speed of $0$ meters per second. (This matches our interpretation). - [D] The height of the object is $0$ meters when the object is traveling at a speed of $0$ meters per second. (The function relates to kinetic energy and speed, not height).

6. Conclusion: The best interpretation of $K(0)=0$ in this context is that the kinetic energy of the object is $0$ joules when the object is traveling at a speed of $0$ meters per second.