This past weekend the boys and girls `Iolani Cross Country teams ran their second race of the season. This weekend’s race, the Kaiser Invitational, was held at Kaiser High School. Kaiser’s course consists of multiple loops around their campus and their fields and is either two miles for Intermediates or three miles for JV and Varsity runners. Although the total distance ran between an Intermediate runner and a JV/Varsity runner differs by about a mile, the total displacement is exactly the same: ~400 meters (the finish line is about 400 meters from the start line).
A photo of me and Ty Moriwaki posing at the starting line.
Upon completing the race, I thought to myself: I wonder what my average velocity and average acceleration was over the course of this race. Well, that’s easy! Your average velocity should simply be your distance divided by time, right? Wrong! In fact, average velocity is only your displacement divided by your time. Knowing this, I can now calculate my average velocity and average acceleration. Given a displacement of ~400 meters and a race time of 20:25 (1,225 seconds) for 3 miles, Vav = 400m / 1,225s: 0.327 m/s. Now that I have my average velocity, I can calculate my average acceleration to be average velocity divided by time, aav = 0.327m/s / 1,225s: 0.000267 m/s^2. Given that the average Intermediate runner can run 3 miles in 13:00 (780 seconds), it may seem puzzling that an Intermediate’s average velocity and average acceleration are higher (0.513 m/s and 0.000658 m/s^2, respectively) than those of a Varsity runner’s, but that’s just simple physics.
A photo of me running toward the finish line at the end of the Kaiser Invitational Varsity race.
A Day in the Life of Physics 