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08 September 2016

AP Physics 1 mail time: Relative motion, and how do you handle calculus-laden responses?

Hibisca, who was in my Walton High School APSI last June, writes:

1. When do you teach relative motion, if you do at all? I could not find any direct references to it in the course description, but there is a multiple choice question in the 2014 practice exam (#35) about frames of reference. I also did not find any direct references to it in your "info to memorize" sheets or other materials.

I don't formally teach it at all... usually a discussion comes up at some point, though.  That #35 is the one about two balls colliding in a moving train car.  I think of it more as a center of mass question -- the center of mass of the two balls keeps going at constant velocity, whether we're observing inside or outside the train car.  (See, I'm phrasing it so "relative motion" doesn't come into play -- just the terminology causes headaches with students, so I try to get the concept without the terminology.)

2. How do you handle students who give answers/explanations with calculus? I can't imagine that would be a common issue on the AP exam, since there aren't any calculations, but I did have an issue on their last quiz where I asked students to determine the final position of an object based on a v-t graph. All of the students except for one used the formula for a triangle; one student set up an integral instead. Do you emphasize the need to approach everything algebraically, or do you give full credit to students who correctly use calculus?

They get full credit, as long as the calculus is clearly communicated.  As you say, the AP question would be "explain how you could determine", and if the student says, "we need to know how far the ball went from its initial position, that's the integral of the velocity function with limits 2 s and 5 s, that works out to 10 m, so add that to the initial position of 1 m to get 11 m final position" that's beautiful.

If you're worried that such a student might not truly understand what he or she is doing, or if the student uses calculus without words and gets huffy when you don't count it right... then the next quiz question might be "explain how to determine the final position of the object" rather than "determine the final position of the object."

Not that you shouldn't have asked them to "determine the final position of the object."  I start there, too.  But then after I'm comfortable that everyone can do the calculation, I insist on the AP Physics 1-level explanation.

More questions about your physics classes?  Send 'em via email, and I may publish as a Mail Time.

1 comment:

1. Excellent points.

Given a choice between spending a day or three on relative motion, I spend it on things they actually need to LEARN now. Your approach to that problem is excellent, because you are looking to see if they choose a definite coordinate system and proceed from there. Learning that some things (velocity, kinetic energy) depend on your choice of coordinate system is the key for now. That prepares a physics major to learn the deeper concepts later on.

My feedback on the v-t graph solution is that it is perfectly fine for a student to exercise their newly found calculus skills -- if they do it correctly so it really is exercise. But they should also notice when doing so is more labor than the alternative. (How about two triangles, where finding the function for the second one from a point-slope formula is more work than just finding the area?) Calculus also leads to the expectation that every integral can be done, because no one assigns ones that can't be done analytically in terms of standard functions. The real world usually requires model building.