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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.
** 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):
10 cm/ 5 sec= 2 cm/sec.
the 10 came from the difference in 10 to 20 cm. the 5 came from the change in seconds from 4 to 9, a difference of 5. quantity a is 10 cm. quantity b is 5 sec. avg rate of change is 2 cm/ 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):
= 10 cm/ sec. quantity A is 30 cm. quantity B is 3 seconds. avg rate is 10 cm/ sec
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In finding the average rate of change of velocity with respect to clock time, the A quantity is velocity and the B quantity is clock time.
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The change in the velocity is from 10 cm/sec to 40 cm/sec. This change is 30 cm/sec, not 30 cm.
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You are given the change in clock time, which is 3 seconds.
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Your calculation
30 cm/sec / 3 sec
is therefore correct (though the 3 sec should be in parentheses), but it isn't completely consistent with your subsequent statements.
The A quantity is not 30 cm, the A quantity is velocity.
The change in the A quantity is not 30 cm but 30 cm/sec.
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If you carry your calculation out, you get
30 cm/sec / (3 sec).
As we will detail soon, the units of this calculation are cm/sec/sec or cm / sec^2, not cm / sec.
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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):
the position changes 50 cm. 50cm/10 sec= 5 cm/sec. 50 cm is quantity a. quantity b is 10 sec. avg rate of change is 5 cm/ sec.
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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 make sure i know this definition by writing it down for refernce until i know it without looking, and do problems in the book to help me become more familar with this definition.
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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):
this definition will be useful in determining rate of change.
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You made some errors but you are logically following the definition, which is something many students have trouble doing at this point of the course. So despite a few errors, which I believe you will easily correct with just a little more practice, you've done well here.
Be sure to see my notes. I'll be glad to answer questions if you have them.
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