Mhy 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.
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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: ********* ********* 2 cm/s (see below)
the quantity A in this problem is position, and qty B is time. So change in A with respect to B is: average rate of change of position with respect to clock time.
( 20 cm - 10 cm ) / ( 9 s - 4 s ) = 10 cm / 5 s = 2 cm/s
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: ********* ********* 10 cm/s (see calculations below). Question: I'm unsure if I did the units correctly - I would have originally thought that I would be dividing by 3 sec, but if doing that I would have come out with 10 cm, and not 10 cm/s. The per second is needed to make the velocity units correct. Did I miss something here?
qty A is = velocity
qty B is = clock time
Change in A with respect to B = change in velocity with respect to clock time = (change in vel) / (change in clock time)
( 40 cm/s - 10 cm/s ) / 3 = 10 cm/s
You are doing the right thing here but your units aren't correct.
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: ********* ********* 50 cm
qty A = position
qty B = clock time
Change in A, with respect to B = (change in position) / (change in clock time) =
5 cm/s = (change in position) / 10 s
(change in position) = ( 5 cm/s ) * 10 s = 50 cm
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: ********* ********* I will ensure that I remember this definition by: 1) writing it down in my notes and reviewing it; 2)applying it in practice problems; and 3) reviewing this particular assignment which I now have saved as a txt file.
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: ********* ********* The procedure I used was to start by naming what A and B are. I then set up the (Change in A) / (Change in B) formula. Once I did that, I inserted the #'s for change in A and change in B to the formula and then solved it. I will remember to use this procedure for the same reasons that I will memorize/know the definition itself: taking notes, reviewing the notes, applying the concepts in practice problems.
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25 minutes
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Very good, except for one error in units.
&#At least part of your solution does not agree with the solution and comments given at the link below. You should view the solution at that link and self-critique as indicated there.
Solution
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