course phy 121
6/4 11:48
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):
average rate of change of A with respect to B = (change in A) / (change in B)
average rate of change of A with respect to B= (10cm)/(5sec)
average rate of change of A with respect to B= 2cm/sec
Your units aren't completely correct here. Be sure to check the discussion in the link given at the end of this document.
In this problem the average rate of change of A refers to the ball rolling backwards and the average rate of change of B refers to the time that it takes for the ball to roll backwards.
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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):
average rate of change of A with respect to B = (change in A) / (change in B)
average rate of change of A with respect to B= (30cm/sec)/(3 sec)
average rate of change of A with respect to B= 10cm/sec
In this problem the average rate of change of A refers to the ball rolling on the track and the average rate of change of B refers to the change in time on the clock.
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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 of change of A with respect to B = (change in A) / (change in B)
average rate of change of A with respect to B= (5cm/sec)/(10 sec)
average rate of change of A with respect to B= 0.5 cm
In this problem quantity A is the position change (5cm/sec) and quantity B is the clock time change (10 sec).
This answer is incorrect. Be sure you compare with the link provided at the end of this document.
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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 is average rate of change of A with respect to B = (change in A) / (change in B). I learn best by making note cards and color coding them. So making note cards and memorizing it is how I will remember it.
Good idea.
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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):
average rate of change of A with respect to B = (change in A) / (change in B)
You would insert the numbers for the change in A and the change in B and then divide them to get you answer. An example of how to apply this formula will go on the back of my average rate of change of A with respect to B note card.
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Please see my notes and submit a copy of this document with revisions and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).Be sure to include the entire document, including my notes.
&#See any notes I might have inserted into your document. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your solutions with the expanded discussion at the link
Solution
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