Wednesday, September 4, 2019

When? Where? A Quick Thought About Kinematics Problems

I was helping a student to work through some simple kinematics problems today, and the following conversation (paraphrased) occurred:

Question on board: A motorcycle is stopped at a traffic light. The light changes, and the motorcycle accelerates steadily at a rate of 3.5 m/s^2 for 4.0 s.... When will the motorcycle's speed be 10 m/s?
Student: Which term is this asking the value of?
Me: Well, the question is asking when an event will occur...
Student: So I am trying to find the distance from the start where the motorcycle will have that speed?
Me: No, that question would be 'Where does the motorcycle reach a speed of 10 m/s, not when will it reach this speed.'

Seeing that the student was still confused, I explained that the word with which we start the question is also a clue for what the question wants us to find (English is this student's native language). What I also realized from this interaction is this: while the wording of the question should give the right clue (when refers to time, where to place), there is a sort of cultural conditioning which we should not ignore. After all, when a child riding in a long car trip asks his parents, "When will we get there?," his mother and father are as likely to answer "in another 10 miles" as to say "in another 10 minutes." Thus, at a young age we are trained to conflate distance with duration.

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