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Phy 231
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: ->->->->->->->->->->->-> n/discussion (start in the next line):
quantity A: position
quantity B: clock time
Ave rate of change in position wrt time = (change in position)/(change in clock time)
=(20cm-10cm)/(9s-4s)
=10cm/5s
=2cm/s
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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: ->->->->->->->->->->->-> scussion (start in the next line):
quantity A: velocity
quantity B: clock time
Ave rate change in velocity wrt time = (change in velocity)/(change in clock time)
=(40cm/s-10cm/s)/3s
=(30cm/s)/3s
=10cm/s^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: ->->->->->->->->->->->-> scussion (start in the next line):
quantity A: position
quantity B: clock time
Ave rate of change in position wrt time = (change in position)/(change in clock time)
5cm/s = (change in position)/10s
50cm*s/s = change in position
50 cm = change in position
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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: ->->->->->->->->->->->-> scussion (start in the next line):
The average rate of change of A with respect to B = (change in A)/(change in B)
The average rate of change of A with respect to B = (change in A)/(change in B)
The average rate of change of A with respect to B = (change in A)/(change in B)
Repetition of all types is the key to memorization. Repeatedly typing the exact wording of the defition, as I've just done a few
times, helps a lot. Then, repeatedly using those exact words whenever I encounter a problem that requires me to use this definition
will help the meaning and purpose of that word-for-word definition sink further in.
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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: ->->->->->->->->->->->-> scussion (start in the next line):
The most significant detail of this definition, I believe, is the phrase With respect to. That key wording tells us the order in
which we plug our numbers into the definition above. I am training myself through these exercises to always be on the lookout for
that phrase; when it appears, it is a signal to apply the procedure as stated.
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*#&!
&#Very good responses. Let me know if you have questions. &#