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 case, if the length is A, and changes from 10 cm to 20 cm, then the change in A would be 10 cm. If B is the time, and changes from 4 seconds to 9 seconds, then the change in B is 5 seconds. By plugging these numbers in to the average rate of change of A with respect to B equation, then 10 cm / 5 cm = 2 cm/sec, which is the average rate of change.
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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): A is the change in velocity (10 cm/sec to 40 cm/sec) which is 30 cm/sec. B in this case is the 3 second time interval. Therefore the average rate of change of its velocity with respect to clock time is (30 cm/sec / 3 sec) or 10 cm/sec.
Good, but the units of the result aren't cm/s. See the link at the end.
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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): Using the formula: 5 cm/sec = change in A / 10 sec, the change in A which is the position change is 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 have made notecards of all pertinent definitions and formulas as extra reminders and study guides.
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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): Determine the two sets of data you are working with, and which will be A and which will be B. Find the change in each. Plug your answers into the equation and solve. I will remember to use this procedure by referring to my notecards or this assignment.
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20 minutes
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Good work, but be sure to see my note above. No revision is necessary as long as you understand how the units work on that one calculation:
&#Please compare your solutions with the expanded discussion at the link
Solution
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