Day 14 – Usain Bolt and Average vs. Instantaneous

Today held the first major quizzes of the year for both classes, which went well overall. In non-AP Calculus, we finished up our intro to derivatives and began exploring the idea of average velocity vs. instantaneous velocity by watching a video of Usain Bolt sprinting (AP Calc listserve idea). I asked the simple question after the video “How fast was he running?” Most students divided distance by time, which made sense, but I asked what kind of speed did they just calculate? Was he running that fast the whole time? What more information do you need to give me more detail? We then looked at data for his 10 m splits during the race to get an idea of how fast he was moving at different points throughout the entire race. Conclusion: using slope is an average velocity, but we can always get better info by making the time interval shorter. We are primed and prepped for the limit definition of the derivative, which will be our whole motivation for studying limits next!