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PHI 241
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: position of ball
Quantity B: change in time
Average rate : 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: ->->->->->->->->->->->-> (start in the next line):
Quantity A: velocity of ball at 1st point
Quantity B: velocity of ball at 2nd point
Average rate: (10cm/s + 40cm/s)/2= 25 cm/s
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@& This is the average velocity, not the requested average rate of change.
You need to methodically apply the definition of average rate of change. Identify the A quantity, identify the B quantity, and follow the definition completely and literally.*@
• 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):
5cm/s * 10s= 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):
I will remember that a rate is what change is measured in and that A comes before B.
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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 first identify the quantities that I need to know. Then I plug in the quantities I know into the formula and solve. I will remember this procedure by remembering that it is always distance over time.
@& The statetement 'the quantities I need to know' is too vague. You need to state specifically how you will identify the quantities and how you will use them.*@
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*#&!
@& You haven't consistently applied the definition of average rate of change to all of these questions.
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