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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: ->->->->->->->->->->->-> (start in the next line):
The rate of change of A, position of ball rolling along a track is 20 cm - 10 cm = 10 cm. The rate of change of B, total time elapse from the ball rolling from 10 cm to 20 cm is 9 sec - 4 sec = 5 sec. Therefore the average rate of change of A with respect to B is 10 cm/5 sec = 2 cm/sec.
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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):
The rate of change of change of velocity is 40 cm/sec - 10 cm/sec = 30 cm/sec. The rate of change of time it took to go from 10 cm/sec to 40 cm/sec is 3 seconds. Therefore the average rate of change of velocity with respect to time = (30 cm/sec)/3 sec = 10 cm.
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@&Good, but (cm / s) / s = cm/s * 1/s = cm/s^2, but the rules for dividing fractions.*@
• 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):
In this question you are finding the change in position, not the average rate of change. To find change of the position = average rate * change of time = 5 cm/sec * 10 sec = 50 cm. So the position changes 50 cm in 10 seconds traveling at 5 cm/sec.
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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):
Memorize: The average rate of change of one quantity with respect to another = (change in first quantity)/(change in second quantity)
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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):
The procedure for applying this definition is to find the difference of each quantity (final value - initial value), then divide the resulting difference of both quantities to find the average rate. You do this each time if you are asked to find the average rate of two quantities. If you find the average rate of A with respect to B, then its (Afinal - Ainitial)/(Bfinal-Binitial).
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*#&!*#&!
&#Good work. See my notes and let me know if you have questions. &#