A long time ago, when I was doing Gorilla Science, I had the idea to do a mathematical physics (specifically mechanics) audio book entirely based on driving. The idea was (is) that drivers would learn both math and physics, from the ground up, all the way to mathematical mechanics and thermodynamics, all just by listening to this thing in the car, and using the car, the roadway, and the other cars around you as the domain. You’d even do experiments while just driving along on your normal commute. The educational theory was (is) that you need to learn things in context (not very original, I know!), and what better context for mechanics (and thermodynamics) can we have than a one ton spherical cow hurtling around tight curves at 50mph.
Anyway, I of course never got around to the audio book, but yesterday I got to cash out one of the central experiments with Leo.
We were headed to campus, about ten miles if I take the long route, which conveniently includes an un-necessary but useful highway segment. So with Leo and Carrie in the back, and me driving, we set out to record our trip. Since Leo’s still not great and writing between the lines (as you’ll get to see in a moment), Carrie sat next to him and actually filled in the table with instantaneous speed and distance every minute, but Leo was watching the clock and reading off the speed and distances from the dashboard. All I did was drive, and occasionally remind him that the minute had turned over.
Here’s what we ended up with:
Now the cool part!
Back at home we started by plotting distance v time.I drew the axes, but Leo labelled them (with a little help), and made the marks (with a little help), and drew the graph (with a little help).
(I’m gonna stop saying “(with a little help)” and you can just read the following as though everyplace I say that Leo did something, it is followed by that phrase!)
The result is the top graph:
You can see where this is going….
The middle table of numbers is the velocity, that is (read on the right) distance/time. Conveniently, we’d used one minute intervals. Actually, I’d suggested 30 seconds, but Leo insisted on one minute, and it turns out that that was very clever, because the denominators are all 1! (I’m sure he didn’t realize that when he insisted on one minute…I didn’t even realize it until we got to this exercise. He did, however, intuit that 30 seconds would have been too busy, and he was right about that!) Since the denominators are all 1.0, we just left them out. So there you have the average speed (per minute) in that segment. And, easy peezy (or however that’s spelled?) do it again, and you have acceleration – we started just writing them as whole numbers instead of having to write zero-point-one before every one of them.
Leo did every calculation on this page — and NOT with ANY help, aside from my helping to keep track of where the next pair of numbers to process was, and I wrote down some of the numbers where they were small, since, as you can tell from the accelerations, Leo’s not too good at writing small numbers (another reason for dropping the decimals).
So there you go: measurement, physics, a little algebra and calculus, all just from a ride to the playground!
(I’d obviously need a different context for relativity and quantum mechanics … how about The Sun! 🙂 )