What is Usain Bolt's velocity as he crosses the finish line?

This activity was designed as an application of the concept of limits. This concept is very technical and students struggle to grasp it. Therefore, having students going through the process of finding a limit in a meaningful way is useful.

This activity requires about 60-100 minutes of classtime + homework, depending on the expected product students are handing in.

The teacher should start by showing the video of Usain Bolt's stunning performance in Berlin in 2009 (for example http://youtu.be/3nbjhpcZ9_g). Then the teacher should ask that simple question: "What is his speed at the exact moment when he crosses the finish line?"

It is very easy to find the average limit of Usain Bolt over the whole race, as we know he ran 100m in 9.58 seconds. But by applying the idea of a limit, students can gradually narrow down the interval to approach a value for the instantaneous speed of Usain Bolt at the finish line.

Students in my class approached the problem in different ways. Some found data on the internet that gave them the answer! (Obviously, we were not the first to ask the question...). This shouldn't be an issue. The end product we expect from students is that they explicitly show the process. The actual result they find is secondary, provided that their reflection is good.

Here are a few screenshots of a student's work to illustrate the idea. A reflection on the process should also be expected to make sure the students formulate and formalize their understanding.