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):
Change in position: 20 cm – 10 cm = 10 cm. Change in time: 9 s – 4 s = 5 s. The average rate of change of position with respect to time: 10 cm / 5 s = 2 cm/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):
Change in velocity: 40 cm/s – 10 cm/s = 30 cm/s. Change in time: 3 seconds. Average rate of change of velocity with respect to time: 30 cm/s / 3 s = 10 cm/s^2.
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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):
If position changes 5 centimeters every second, if 10 seconds pass, the position changes by 5*10 = 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 can remember that the average rate of change of quantity A to quantity B is equal to the change in A divided by the change in B by thinking of it in simple terms that I know intuitively. I can think of it, for example in terms of velocity. Velocity is equal to the change position divided by the change in time. I also know this intuitively, because I know that velocity is frequently measured in meters per second (m/s) and miles per hour (mph).
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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):
To apply this definition, I will indentify the quantities A and B and determine the change in each. Then I will determine how to compare them using the average rate of change definition and then divide them. I can remember how to apply this procedure by remembering the definition of average rates of change and filling in the values needed.
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15 minutes
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&#Very good responses. Let me know if you have questions. &#