Final answer:
The stopping distance at 60 mph is four times greater than at 30 mph due to the quadratic relationship between speed and stopping distance, as derived from the equation of kinetic energy and the work-energy principle.
Step-by-step explanation:
The student's question addresses the relationship between speed and stopping distance in a physical context, which is a concept covered by physics, specifically kinematics. The answer to the question “At 60 mph, it may take you __ as far to stop as it does at 30 mph, (even though your speed has only doubled)” is D) Four times. Stopping distance increases with the square of the speed, meaning if you double your speed from 30 mph to 60 mph, it takes four times as much distance to stop due to the kinetic energy being quadrupled at 60 mph compared to 30 mph. This concept is derived from the equation for kinetic energy, KE = ½mv2, and the work-energy principle that states the work done to stop the vehicle is equal to the kinetic energy the vehicle has before decelerating to a stop.