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phy 201
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.
** CQ_1_01.1_labelMessages **
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: ->->->->->->->->->->->-> (start in the next line):
a=cm
b=seconds
(20cm-10cm) / (9sec-4sec)
=10cm/5sec
=2cm/sec
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• 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: ->->->->->->->->->->->-> (start in the next line):
40cm/sec- 10cm/sec=30cm/sec
30cm/3sec=10cm/sec
I was a little unsure of how to approach this. I didn’t know whether to use 30cm/3sec or use 30cm/sec * 3sec…How do you work this one???
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You need to follow the definition, which requires that you divide the change in velocity by the change in clock time.
What is the change in velocity (you calculated this correctly)?
What is the change in clock time?
What therefore is change in velocity / change in clock time?
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• 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: ->->->->->->->->->->->-> (start in the next line):
5cm/sec = x cm/10sec
50=x
50 cm
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Proportions are good, but you want to think in terms of rates.
ave rate of change of pos with respect to clock time is (change in position) / (change in clock time),
which can be written in abbreviated form as
ave rate = `ds / `dt
It follows that
`ds = ave rate * `dt = 5 cm/s * 10 s = 50 cm.
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• 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: ->->->->->->->->->->->-> (start in the next line):
I will remember this definition by reviewing the formula, practicing problems pertaining to the formula, and keeping notes for better understanding.
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• 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: ->->->->->->->->->->->-> (start in the next line):
The average rate of change of one quantity with respect to another can be put this way
The average rate of change in A with respects to B
=(change in A) / (change in B)
Ill remember this procedure by continuous practice and by recognizing when a problem includes the words “average rate,” “with respect to,” and more.
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&#Good responses. See my notes and let me know if you have questions. &#