Phy 121
Your 'cq_1_01.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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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: ->->->->->->->->->->->-> : Quantity A = 20 cm – 10 cm = 10 cm
Quantity B = 9 seconds – 4 seconds = 5 seconds
Average rate = (10 cm) / (5 seconds) = 2 cm/second
• 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: ->->->->->->->->->->->-> : Quantity A = (40 cm/second) – (10 cm/second) = 30 cm/second
Quantity B = 3 seconds
Average rate = (30 cm/second) / (3 seconds) = 10 cm
• 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: ->->->->->->->->->->->-> : Quantity A = unknown
Quantity B = 10 seconds
Average rate = 5 cm/second
Ave. Rate = (change in A) / (change in B)
5 cm/second = (change in A) / (10 seconds)
(5 cm/second) * (10 seconds) = change in A
50 cm = change in A, so the position changes by 50 cm
• 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 remember this definition by associating it with the formula for finding slope of a line (Y2 – Y1)/(X2 – X1) because that is immediately what it reminded me of.
• 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: ->->->->->->->->->->->-> : In order to apply the definition, you first have to decide which components of the problem are A, B, and the average rate of change. Whichever one is not given in the problem is what must be found. Then it is simply a matter of plugging the values into the equation to solve for the missing variable. I will remember to apply this procedure because it is a basic formula.
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15 minutes
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&#Very good responses. Let me know if you have questions. &#