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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.
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Asst 1 Question 1
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):
(20 cm - 10 cm) / (9 s - 4 s) = 10 cm / 5 s = 2 cm / s
2 cm per second
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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):
(40 cm / s - 10 cm / s) / 3 s = (30 cm / s) / 3 s = 10 cm / (s^2)
It accelerates at a rate of 10 cm per second every second.
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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):
5 cm / s = n cm / 10 s
n cm = 10 s × 5 cm / s
n cm = 50 cm
n = 50
The position changes by 50 cm.
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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):
So basically I'm not trying to simplify the problem. An average is a quotient of a product of two terms, where the average is expressed in the likeness of either initial term of the product if and only if the average term is a product of two terms as well; otherwise, it is a just simple quotient. I'm not so sure what you want. I guess generalized.
Here's an idea. Instead of telling me that it is going to get in the way of my existing logic, show me where a misconception occurs. I don't see myself making goofy mistakes because I do try to reason things. (It's always stupid things that mess me up, like missed a digit here or didn't think about what I was writing.) It may however offer the fallacy of failing to incite a speculation from the clues of a puzzle when such a speculation is right to do so; i.e. failure to use may fail to solve the problem without an original conception.
It just seems like such a simple thing to sound so complicated. If it's logic I need, I'm in good shape to keep on trucking.
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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):
I know that what I need to know is that there is an Exhibit A and an Exhibit B. Together the product yields an Exhibit AB. As long Exhibit AB is respective to either Exhibit A or Exhibit B (it is by definition, but assuming a variable Exhibit AB toward a reference Exhibit A or Exhibit B) then the following rule applies:
Average rate of change of A respective to B is the same as the change of A versus the change of B.
Conversely:
A change of A as part of a change of B is the average rate of change in A with respect to B.
Looks to me like the whole thing is that the average (which is a proportion) is important because it applies to change type1/change type2->average change type1/type2. Maybe I just get it. Let me know if I'm not quite there with it.
I suspect you are in good shape with the definition.
There will be plenty of exercises related to the definition, and plenty of opportunity to test your understanding. I'll give you feedback if anything is amiss.
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20-30 mins maybe
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&#Very good responses. Let me know if you have questions. &#