I’ve done this activity once before, and I wrote about it here, but I’m continuing to tweak it. In the late 1800s, Eadward Muybridge published several time-lapse photo essays of animals and people in motion. Because he used a background with a grid on it, it is easy to see how much distance the subject covers in between each frame (which are snapped at 0.031 sec intervals). This sets up a great lesson on calculating average velocity, and approximating instantaneous velocity!
While I still asked my students to plot the cat’s position vs. time by hand, we also used the desmos online grapher to plot the data as verification of their work. It was great to see the light bulbs go off in my students’ heads as they worked out difference quotients for smaller and smaller time intervals.
Here’s the plot generated using desmos:
We had an excellent discussion of how the cat’s motion breaks down into two distinct parts, and how the slope of each corresponds to the velocities of the cat walking and running.
Once again, I must thank Dr. Nell Rayburn, Professor and Chair of Mathematics at Austin Peay State University for sharing this activity with other calculus teachers in Tennessee. Here are her original documents: Cat Photos, Muybridge Cat Worksheet, Muybridge Cat Key.