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.
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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: ->->->->->->->->->->->->
The average rate of change would be 20-10(A) over 9-4(B) so 10 over 5 equals 2cm per second
• 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: ->->->->->->->->->->->->
40cm/s – 10cm/s(A) over 3(B) equals 10cm/s
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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: ->->->->->->->->->->->->
The average rate is equal to A over B(what is in respect to): therefore this would 5cm/s = change/10 seconds. The position changes 50cm
• 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 am going to write it down in my notes so that way when I study I will be able to look at it and also the more I practice these problems the more familiar I will become with it and I will be able to memorize the problem.
• 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: ->->->->->->->->->->->->
First read what the question is asking. Second determine what is changing in respect to the other. Finally, what ever is changing is on the numerator and what the problem is in respect to is the denominator. This will equal the average rate of change.
I will remember this by practicing problems and also pick out what the question is asking for in terms of the average rate or if it wants one of the variables.
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20 minutes
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&#Please compare your solutions with the expanded discussion at the link
Solution
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