Rpm-Gps

Over Christmas I was driving from Toronto to Kingston. I had the route finder working and it was happily doing its route-finding thing. But that’s not all it was doing; it was telling me how the traffic was and what the weather was, and it warned me when I deviated from my lane, and other useful things. It also gave me my speed, and the occasional warning if I exceeded the speed limit too much.

But then I noticed something curious. The speed indicated on the car’s speedometer was around 110 km/h. But the speed registered by the GPS was around 105 km/h. And even when the speeds varied a bit, the difference remained fairly constant at about 5 km/h. That was interesting. What might be the cause of that?

This is an interesting modeling problem that involves different kinds of thinking. It’s very much a discussion problem as the kids are essentially asked to tell the story themselves—the story of how things work.

Our target audience is grade 9.

I tell the story to a grade 9 class and ask for ideas. I tell them they need to think mechanistically. The two measures of speed are generated in a different way. What exactly might those two ways be? And how do they work?

That sets us off on a fascinating journey. The math is simple enough, but we need to think clearly about what it tells us.