phy 121
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The problem:
Here is the definition of rate of change of one quantity with respect to another:
The average rate of change of A with respect to B on an interval is
average rate of change of A with respect to B = (change in A) / (change in B)
Apply the above definition of average rate of change of A with respect to B to each of the following. Be sure to identify the quantity A, the quantity B and the requested average rate.
If the position of a ball rolling along a track changes from 10 cm to 20 cm while the clock time changes from 4 seconds to 9 seconds, what is the average rate of change of its position with respect to clock time during this interval?
answer/question/discussion:
Change in A is 10cm and the change in B is 5seconds, which means that the average rate of change is 2.
Good, except that 10 cm / (5 s) = 2 cm/s, not just 2. Correct units are essential.
If the velocity of a ball rolling along a track changes from 10 cm / second to 40 cm / second during an interval during which the clock time changes by 3 seconds, then what is the average rate of change of its velocity with respect to clock time during this interval?
answer/question/discussion:
Change in A is 30 cm/second which means that the average rate of change is 10.
The units are essential. What are the units of (30 cm/s) / (3 s)?
If the average rate at which position changes with respect to clock time is 5 cm / second, and if the clock time changes by 10 seconds, by how much does the position change?
answer/question/discussion:
Since the average rate of change is 5 cm/second and the clock changes by 10 seconds than the position changes to 50cm because it changes at the rate of 5cm per second.
You will be expected hereafter to know and apply, in a variety of contexts, the definition given in this question. You need to know this definition word for word. If you try to apply the definition without using all the words it is going to cost you time and it will very likely diminish your performance. Briefly explain how you will ensure that you remember this definition.
answer/question/discussion:
I will be sure to memorize this definition so that I can be sure to perform well.
You are asked in this exercise to apply the definition, and given a general procedure for doing so. Briefly outline the procedure for applying this definition, and briefly explain how you will remember to apply this procedure.
answer/question/discussion:
I will remember this procedure by memorization, so that I can apply this definition in the future
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about 15 minutes
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Good, except for the omission of units on a couple of answers.
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