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
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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.
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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: A (20 cm - 10 cm) / B (9 s - 4 s) = 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: A (40 cm/s - 10 cm/s) / B (3 s) = 30 cm/s / 3 s = 10 cm for every 1 second of elapsed time
This would be 10 cm/s for every second of elapsed time. The unit of your answer would therefore be (cm/s) / s, or 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: A / B (10 s) = 5 cm/s; A = (5 cm/s) * 10 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: (change in A) / (change in B) = average rate of change of A with respect to 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: Take the difference of the two quantities for distance and divide that by the difference of the two time intervals. This will give the average rate of change of one quantity with respect to the other.
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15 minutes
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You did a very good job of relating the definition to the solution of the problem. The only error I've noticed is that you did not have the correct units on one of your calculations. Be sure you see my note and let me know if you don't completely understand the unit calculation and the units of the result.