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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 **
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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):
Quantity A is 20-10=10cm and Quantity B is 9-4=5sec. the average rate of its position with respect to the clock time is 2cm/sec.
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You definitely have the right idea, and your final result is correct. However your terminology does not quite fit the definition of average rate, and it's avoids a lot of confusion in upcoming assignments to get the terminology correct from the very beginning.
The average rate of change of quantity A with respect to quantity B is (change in A) / (change in B).
Using the terminology of your solution your calculation would have been Quantity A / Quantity B.
The problem is that what you identified as Quantity A was in fact the change in quantity A; similarly for Quantity B.
As a result you got the right answer, but with not-quite-correct terminology.
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The following statement, modified from yours with just a added few words, is correct:
The change in quantity A is 20-10=10cm and the change in quantity B is 9-4=5sec. the average rate of its position with respect to the clock time is 2cm/sec.
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In any case, quantities A and B would be identified by their names. Quantity A is position, and quantity B is clock time.
With this terminology the definition is a perfect fit.
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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):
the average would be 10cm/s. Quantity A would be the difference between 40 cm to 10cm which is 30. Quantity B would be 3 sec. because it is the change in time. So then you divide 30/3 to get 10cm/s.
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See my preceding notes.
For example:
Quantity be is clock time, not change in clock time.
3 sec is the change in clock time, so it is the change in quantity B; it is not quantity B.
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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):
it would be 2. Because you know that average rate is 5cm/s then you can make a proportion out of the rest to find the miss part.
5cm/1s=10s/x
5cm*X=10s
X= 10/5cm
X=2cm
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I do not recommend using proportion with this definition. You want to think in terms of quantities, rates, changes, etc..
How would the definition of average rate be used to answer this question?
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Note also that you have used an inverse proportionality in a situation that calls for direct proportionality.
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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):
the average rate of something takes 2 quantities: The change in quantity 1 divided by quantity 2.
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This is a good statement.
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You are doing a good job of applying the rate definition. You have the idea and are using it correctly. However you do need to be very precise with the terminology.
Also you don't want to solve that last question using proportionality. You need to use the definition of rate.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes. &#
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