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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): In this situation, the quantity A will be the position of the ball and the quantity B will be the time.
The ball moved from 10 cm to 20 cm, a change in position of 10 cm. While the ball was moving, the clock time changes from 4 seconds to 9 seconds, a change of 5 seconds.
Applying the equation given, average rate of change of A with respect to B = (change in A) / (change in B), I write
10 cm / 5 seconds = 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 quantity A will be the change in velocity and the quantity B will be the change in time. There is a 30 cm/sec change in velocity over 3 seconds.
Using the given equation, average rate of change of A with respect to B = (change in A) / (change in B), we write
30 cm/sec / 3 sec = 10 cm/sec^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): In this situation, the quantity A is the position change and the quantity B is the clock time. We can simply plug what we know into the equation given.
Average rate of change of A with respect to B = (change in A) / (change in B)
A(position) / 10 seconds = 5 cm / second
Multiplying each side by 10 we get, A = 5 cm/sec * 10 sec
A = 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): To ensure that I will remember the definition of the rate of change of one quantity with respect to another, I will write the definition down in a place I can easily reference for future study.
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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 the definition, average rate of change of A with respect to B = (change in A) / (change in B), I must find the change in A and B of the given quantities by subtracting the initial measurements from the final measurements. Following that, I must divide the change in A by the change in B to calculate the rate of change of A with respect to B.
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20 minutes
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&#Your work looks very good. Let me know if you have any questions. &#