Back in the summer, I did a post mathematically comparing two routes to campus, one with a small number of traffic lights, the other with a larger number of stop signs, and looked at which would be faster. Later on, I did the experiment, too.) Having spent a bunch of time on this, I was thinking about whether I could use this as a problem for the intro physics class. I decided against it last fall, but something else reminded me of this, and I started poking at it again.
So, I played around a bit with some numbers, and came up with the following possible framing for a question. I’ll throw this out here, to see what people think, then I’ll post some solutions in a few hours.
A car starts from rest at the beginning of a straight 1km course, accelerates up to some speed, cruises at constant speed for a while, then decelerates to a stop at the end of the course. A second, identical car does the same course, but decelerates to a stop at the halfway point. It then immediately accelerates back to its cruising speed, and then decelerates to a stop at the end of the course.
How much faster does the second car have to go in order to complete the course in the same time as the first car?
Obviously, this requires some assumptions about the speed and acceleration of the car, which might make for some useful discussion. You can find the necessary math at the first link above, if you want to work it out. For a class using a clicker-type response system, I’d turn it into a poll question like so:
So, we’ll leave this up for a while, and then this afternoon, I’ll post some analysis. Feel free to share your thoughts about appropriate assumptions, etc. in the comments. Or to suggest ways to re-cast the problem that might be more useful. This is classical physics, though, so you don’t get to choose more than one option.