It’s just that it’s the wrong way round with speed on the dependent axis making it the inverse of the quadratic kinetic energy equation, n’est-ce pas? That’s the one tiny thing I didn’t like about this as to me skid length should be a function of speed, the independent variable, but that’s me in full-on hair splitting mode… Great bit of work yet again Dan.

I took some time to re-frame this problem in another way. I don’t know how to produce the third act in a way that would interest kids, although maybe I could use the first three speeds as the data, and the final speed to frame the question.

See http://davidwees.com/content/three-acts-stopping-distance-makeover

I’d love to work something like this in if possible.

Evaluating the formula to fill out the table is boring, but not a slam dunk for many students. Solving for a variable under a radical is not easy even if students have seen it before. And, if they haven’t seen it before, would certainly qualify as “critical thinking”. The revision is an easier question — recognizing that speed is related to skid length, using sliders to fit a provided form, and solving graphically.

The Trooper Bob stuff is a bit silly. The purpose of extending the graph is to see what happens. Does it get flatter, less flat, will it ever be horizontal, will it turn around, will it rise above 100 mph? Maybe also look at whether it is a better predictor for high speeds or low speeds by plotting the actual data along with the curve.

http://forensicdynamics.com/stopping-distance-calculator

(or maybe help them buid a model using more data besides the three pictures)

Another interesting thing to done would be to recreate the program that runs in that web page using a spreadsheet or basic programming (depending on the programming skills of the kids).

Looking forward to reading comments here since I am not satisfied with my revision.

Dan, is your first picture – the wreck where students estimate the speed copyrighted? I might like to use that one if I pursue this problem.