Illustration: Do not answer these problems, COMPARE them.

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.
• Carols problem gave two displacements.
• Joans problem gave two positions.
• Both positions and displacements tell where, but
  NOT IN THE SAME WAY.

5

• Both problems gave two time values.
• Carols problem gave two time durations.
• Joans 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 wont confuse you.

8

• IF YOU JUST MEMORIZE THE FORMULA BECAUSE YOU
  DONT 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.