No Speed at 52 mph

This is from an online pre-class assignment:

Here is a physics problem! Imagine you are driving a car along a long straight. Your friend in the passenger seat is recording where you are every hour of the trip.

 Clock Reading   Mile-marker 

2:00 PM

20

3:00 PM

72
4:00 PM

124

5:00 PM

???

6:00 PM

228

Explain why your friend might reach the conclusion that the speed of the car at 3:00 PM was 24 miles/hour.

Then explain why that answer is probably not correct.

Student Response:

Well someone might get 24 miles/hour by dividing the mile marker (72) and the given time (3:00 PM) and think that would be the miles traveled in that hour. But just because you are at a given mile marker that does not tell you speed because you are at that mile marker for only an instant, so it would be calculated as no speed.

  1. What is the student thinking? Why do think it made sense for the student to write this answer?
  2. What other knowledge and experiences might we presume the student has for thinking about this question? Why do you think the student failed to draw on this knowledge when answering the question?
  3. What question or problem would you pose next to help the student make the next step toward understanding?
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2 comments

  1. Ben Wildeboer (@WillyB)

    First, I really like the format of the question, that requires students to think about another “student’s” thinking. I suppose it’s also why I’m a big fan of the Mistake Game.

    I wonder if the student answered there is “no speed” because (s)he’s thinking about the singular instant that the car is at mile marker 72- and thus is thinking that the change in position at that instant is zero and/or the change in time at that instant is zero. Thus the speed is zero at mile marker 72.

    Perhaps having the student draw a position-time graph would help, since that would come out as a nice straight line showing that the speed of the car is constant, and then have them figure out what the slope of that long straight line is?

    FWIW- as someone who will be teaching physics for the first time in quite awhile next school year I’m very much enjoying this blog and the analysis in the comments. It’s a bit intimidating since I clearly don’t have the analysis & support skills the contributors have, but I’ve already found it very helpful just as an exemplification of how to use student mistakes to drive the next step in instruction. That’s something that often gets talked about as a good practice but is rarely demonstrated as clearly as it is on these pages. This is Good Stuff.

  2. Max Goldstein

    I hate to sound like a broken record, but we see once again the difference between t and delta-t. This time, the student is aware that it’s a mistake to divide the mile marker by the clock time.

    But the real student’s real error is another thing entirely. I smell a whiff of Zeno’s paradox: at the infinitesimally small instant that the car is at the marker, there can be no motion. The student fails to do a “common sense” check or “ballpark estimate”. Maybe the teacher should ask what the speed is between 2 and 3 pm.

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