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: A is the position of the ball while B is the time in seconds. The rate of change would be 10 / 5 which is equal to 2.
• 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 would be the cm/second while B is the time in seconds. The average rate of change would be 30 / 3 which is equal to 10.
• 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 would be the position change, while B is the clock time change. The average rate of change is given at 5cm/second. To find A, you must multiply B by the average rate of change. That means A is equal to 10* 5 which equals 50.
• 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: The average rate of change with respect to A on B is the change in A over the change in B. This is a basic definition that is used everywhere and so it is important to remember.
• 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: An outline would be: If the ( A variable ) changes from X to Y while the ( B variable ) changes for X to Y, then what is the rate of change of the system?
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20 minutes
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