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Illustration: Do not answer these problems, COMPARE them.

Illustration: Do not answer these problems, COMPARE them. Carol is out driving. Starting from town at 9 AM she drives 20 km south in 20 minutes. Then she drives 40 km north in 30 minutes. What is her average velocity for the described motion?

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Illustration: Do not answer these problems, COMPARE them.

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  1. Illustration: Do not answer these problems, COMPARE them. • Carol is out driving. Starting from town at 9 AM she drives 20 km south in 20 minutes. Then she drives 40 km north in 30 minutes. What is her average velocity for the described motion? • Joan is out driving. At 20 minutes after 9 AM she is 20 km south from town. At 30 minutes, she is 40 km north of town. What is her average velocity for the described motion?

  2. Are there PHYSICAL QUANTITY VALUES that are DIFFERENT for Carol and Joan? • Are there VALID FORMULAS that are true for Carol but false for Joan, or false for Carol but true for Joan? (Note: Having unknowns does NOT make a formula false, but it may make the formula useless.) • Are the QUESTIONS about Carol and Joan different? • Are the ANSWERS about Carol and Joan different? • The answers: No, No, No, Yes

  3. Conclusion? • The given VALUES are the SAME. • The valid FORMULAS are the SAME. • The QUESTIONS are the SAME. • BUT THE ANSWERS ARE DIFFERENT. • BECAUSE THE VALUES GIVEN ARE FOR DIFFERENT, BUT SIMILAR, CONCEPTS.

  4. The values in the problems provided “where” and “when” information. • Carol’s problem gave two displacements. • Joan’s problem gave two positions. • Both positions and displacements tell where, but NOT IN THE SAME WAY.

  5. Both problems gave two time values. • Carol’s problem gave two time durations. • Joan’s problem gave two times when. • Both tell when, but in different ways.

  6. These are two out of MANY ways where the SAME VALUE can have DIFFERENT MEANINGS, due to a different context. • As students you need to be learning to recognize when a situation is giving you a value that is related to, but is not, the standard usage.

  7. IF YOU UNDERSTAND THE CONCEPT, if you have worked with it enough to understand it, then the formulas will be easy to remember because they just express the concept mathematically. • Further, the variety of ways to express similar information won’t confuse you.

  8. IF YOU JUST MEMORIZE THE FORMULA BECAUSE YOU DON”T FULLY UNDERSTAND THE CONCEPT, then Murphy will make sure you get a problem (on the test, on the job) for which the formula will look OK but the formula will give you the wrong answer. • (And I WILL give Murphy a hand, because I want you to learn the concept, not just the formula.) • Maybe worse: If he can, Murphy will let you misremember the formula on the few times when it would work.

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