Final answer:
The independent quantity is time, and the dependent quantity is the distance Sophia covers. The function representing Sophia's walk to the mall is D(t) = 3t. This describes a linear relationship between time and distance, mirroring the formula for constant velocity in translational motion.
Step-by-step explanation:
In the problem given, Sophia is walking to the mall at a rate of 3 miles per hour.
To identify the independent and dependent quantities, we must understand that the independent variable is the one that we have control over or that changes on its own, while the dependent variable is the one that depends on the independent variable.
In this scenario, the independent quantity is the time spent walking because it is the variable that can change independently.
The dependent quantity is the distance Sophia covers because it depends on how much time she has been walking. Therefore, the function representing the problem will be D(t) = 3t, where D is the distance in miles and t is the time in hours.
To solve for the unknown, one would simply need to substitute the given time into the function to find the distance Sophia has walked.
In terms of a translational analog, we are dealing with a linear relationship where the velocity (speed) is constant, akin to simple translational motion where velocity equals displacement over time.