Corvettes, Curve Fitting, and Calculus

• # Corvettes, Curve Fitting, and Calculus

A nonroutine task with three hallmarks of a good problem offers the flexibility to model real-life, messy data.
Sometimes the best mathematics problems come from the most unexpected situations. Last summer, a Corvette raced down our local quarter-mile drag strip. The driver, a family member, provided us with time and distance-traveled data from his time slip (see fig. 1) and asked us, “Can you calculate how many seconds it took me to go from 0 to 60 mph?” Although we initially thought that this question was a straightforward one, we soon discovered that, depending on the solution strategy and assumptions, different answers were possible. Thus began the ongoing discussions with our colleagues—and with high school mathematics teacher friends over pizza and with mechanical engineer family members at holiday dinners—to collectively decide on the “best” method. The mathematical discussions that arose on how to best solve the problem (fig. 2) prompted us to ask two questions: (1) What makes this problem so intriguing? and (2) What would students do?