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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.
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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: ->->->->->->->->->->->-> (start in the next line):
Assign the A value of distance and B the value of time.
average rate of change of A with respect to B = (change in A) / (change in B)
average rate of change of dist with respect to time = (change in dist) / (change in time)
(change in dist)=20cm-10cm=10cm
(change in time)=9sec-4sec=5sec
average rate of change of its position with respect to clock time during this interval=10cm/5sec or 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):
A=change in velocity= 40cm/sec-10cm/sec=30cm/sec
B=change in time=3sec
average rate of change of A with respect to B = (change in A) / (change in B)
average rate of change of velocity with respect to time = (30cm/sec) / (3sec)
average rate of change of velocity with respect to time=10cm/sec^2
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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):
average rate of change of A with respect to B = (change in A) / (change in B)
average rate of change of position with respect to time = (change in position) / (change in time)
5cm/sec=change in position/10sec
Change in position=50cm
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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 think of this as the formula for the slope of a line. The formula for the slope of a line is the change in y over the change in x. We just need to assign the values to x and y. Also I assign the words of the average rate of change to the word slope. Finally I can see that there is a pattern of A B A B.
The average rate of change of A with respect to B is (change in A)/(change in B)
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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):
First I would identify what the 2 things that are going to be my A or B or change in A or B. Then I would write out the definition and substitute the values into the definition. Finally I would solve the problem to find the missing piece of information.
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30min
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Submitted on 9-8-10
Very well done.
&#See any notes I might have inserted into your document. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#