Phy 201
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; quantity B: time; average rate = velocity or speed
Average rate of change = (20cm-10cm) / (9s-4s) = 10cm / 5s = 2m/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: change in speed; quantity B: time; average rate = acceleration
Average rate of change = (40cm/s-10cm/s) / 3sec = 30cm/s / 3 sec = 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):
Average rate = change in position / change in time
5 cm/sec = change in position / 10 s change in position = 10 s * 5cm/s = 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):
The definition of the average rate of change is the change in the first quantity divided by the change in the second quantity. It is the slope of the line between those two points with the ‘with respect to’ quantity on the bottom of the fraction—quantity 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):
To use the definition of the rate of change, you take the main quantity, whatever the dependent variable is, find the difference or the change between the two values. Then, you take the independent variable, quantity B, find the change between those two points and put it on the bottom of the fraction. Then you simplify and you have the average rate of change.
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6/5 3:30
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20 minutes
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&#Good responses. See my notes and let me know if you have questions. &#