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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):
Average change of position with respect to clock time
10 cm - 20 cm/ 4 sec - 9 sec = -10cm / -5sec = 2 cm per 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):
average change of velocity with respect to clock time
10 cm per second - 40 cm per second / 3 sec = -30 cm per second / 3 sec = -10 cm per second per second
?????????????????? When doing the rate of change do you always subtract the numbers so that you get a positive number or do you subtract them like I did in the sequence of the problem. Also the units confuse me. Is cm per second per second make sense??????????????????????
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@& cm / sec / sec makes perfect sense; it tells you by how many cm/s the velocity is changing, on the average, for every second that passes.
The best practice is to always subtract the initial value from the final value of each quantity. You would get the same thing if you subtracted the final from the initial for each quantity, but you would in an important sense be thinking backwards.
The fatal error would be to do the A quantity one way and the B quantity the other. You would get the negative of the correct answer and your thinking would be significantly confused.*@
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):
(5 cm/ second = x / 10 sec) 10 sec
50 cm = the amount that the position changed
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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 that average the rate of change of A with respect to B on an interval is the change in A divided by the change in B. I will remember this by remembering that the A and B go in alphabetical order. I will also remember to look for the words with respect to. Because whatever follows with respect to is usually B and whatever precedes it is normally A.
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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):
Apply the definition by first finding what quantity A is and what quantity B is. I will remember the phrase with respect to because whatever follows with respect to is usually B and whatever precedes it is normally A. You might have to subtract 2 quantities to find A or B since the average rate of change is the change in A over the change in B. Then you divide A/B.
I will remember this using the same techniques listed above and by remembering that a keyword is really change which clues me into remembering that the formula is change in A / change in B.
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@& This looks good.
No revision is necessary, but you should take a couple of minutes to read the discussion in the link given below.
&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new 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. &#
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