#$&*
Phy 121
Your 'cq_1_01.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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The problem:
Here is the definition of rate of change of one quantity with respect to another:
The average rate of change of A with respect to B on an interval is
• average rate of change of A with respect to B = (change in A) / (change in B)
Apply the above definition of average rate of change of A with respect to B to each of the following. Be sure to identify the quantity A, the quantity B and the requested average rate.
• If the position of a ball rolling along a track changes from 10 cm to 20 cm while the clock time changes from 4 seconds to 9 seconds, what is the average rate of change of its position with respect to clock time during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
#$&*Quantity A is the position of the ball along the tracks. Quantity B is the change in the clock time. Average rate if change=(Change in A)/(Change in B)
Average rate of change=(20-10)/(9-4)
Average rate of change=10/5 The Average rate of change=10 cm/5s
I believe I understand this problem. Just set the problem up and then do the math that is involved.
• 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):
#$&*Quantity A is the ball rolling along a track with respect to Quantity B which is the three second change in the clock time. Average rate of change(40cm-10cm)/(3s)
40 cm and 10 cm are not quantities associated with this calculation. 40 cm/s and 10 cm/s are. This changes the units of your answer.
Average rate of change=30cm/3s
This can be simplified to 10cm/1s
I believe that I also understood this problem. I set the problem up then did my math and simplified at the end to get my answer.
• If the average rate at which position changes with respect to clock time is 5 cm / second, and if the clock time changes by 10 seconds, by how much does the position change?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
#$&* I am trying to figure out Quantity A while Quantity B is the 10 second time change and the average rate of change is 5cm/second.
5cm/1s=(A)/10
Then multiply both sides by 10 to get A=50cm/10s The position changes 50cm in 10 seconds.
Very good application of the reasoning. However note that when you multiply both sides by 10 s, you get 50cm/s * 10s, not 50 cm / 10 s. The result is 50 cm, as you say; just be careful about those little details.
This problem was a little confusing. I was given the rate of change and the second quantity and I was asked to find the first quantity. I set up the problem and multiplied the rate of change by the second quantity.
You reasoned it out beautifully.
• 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):
#$&* I will write the definition of the average rate of change of A with respect to B=(change in A)/(change in B) in my notebook and I will memorize it and I can look back to my notebook if I need refreshing on it. If I got the three problems above correct then I think I know how to use the definition also.
• You are asked in this exercise to apply the definition, and given a general procedure for doing so. Briefly outline the procedure for applying this definition, and briefly explain how you will remember to apply this procedure.
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
#$&* I would apply this definition when I am trying to find the change in one quantity which is influenced by another quantity. Then I would find the change by dividing the change in the first quantity by the change in the influencing quantity.
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1 hour
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You are using the definitions extremely well. See my notes on some of the details.
Note on future assignments that your answers are to go before, not after the #$&*.
You don't need to revise or submit anything more on this question, but do see the link below to reinforce your application of the reasoning as well as correct some of the details.
&#See any notes I might have inserted into your document. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your 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. &#