#$&*
Phy 231
Your 'cq_1_01.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
The problem:
Here is the definition of rate of change of one quantity with respect to another:
The average rate of change of A with respect to B on an interval is
• average rate of change of A with respect to B = (change in A) / (change in B)
Apply the above definition of average rate of change of A with respect to B to each of the following. Be sure to identify the quantity A, the quantity B and the requested average rate.
• If the position of a ball rolling along a track changes from 10 cm to 20 cm while the clock time changes from 4 seconds to 9 seconds, what is the average rate of change of its position with respect to clock time during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
Quantity A = position
Quantity B = time
Quantity A = final – initial; Quantity A = 20 cm – 10 cm = 10 cm
Quantity B = final – initial; Quantity B = 9 s – 4 s = 5 s
Average Rate = Quantity A / Quantity B
Average Rate = 10 cm / 5 s = 2 cm/s
#$&*
• 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):
Quantity A = velocity
Quantity B = time
Quantity A = final – initial; Quantity A = 40 cm/s – 10 cm/s = 30 cm/s
Quantity B = final – initial; Quantity B = 3 s – 0 s = 3 s
Average Rate = Quantity A / Quantity B
Average Rate = (30 cm/s) / (3 s) = 10 cm/s^2
#$&*
• If the average rate at which position changes with respect to clock time is 5 cm / second, and if the clock time changes by 10 seconds, by how much does the position change?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
Quantity A = position
Quantity B = time
Average Rate = Quantity A / Quantity B
Average Rate = 5 cm/s; Quantity B = 10 s; Quantity A = ?
5 cm/s = Quantity A / 10 s
Quantity A = (5 cm/s)*(10s) = 50 cm
#$&*
• 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 will write it down and look at it every day. I will also write it on a piece of paper that I’m going to use as a reminder of what formulas or definitions I need to memorize and know how to apply.
#$&*
• You are asked in this exercise to apply the definition, and given a general procedure for doing so. Briefly outline the procedure for applying this definition, and briefly explain how you will remember to apply this procedure.
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
When deal with the rate of change of one object with respect to another, you must first ask yourself what is rate of change. When deal with rate of change of Quantity A with respect to Quantity B, the rate of change = Quantity A / Quantity B. Then you must decide what quantity A is and what Quantity B is based on the information given in the question. After you figure out this information you can then plug in the information into the equation for rate of change and solve the equation to come out with an answer. I will remember this definition by writing it down on a piece of paper that I’m going to use as a reference to definitions and equations I need to remember. I will review this paper every day and use it to review for exams.
#$&*
** **
About 15 - 20 min.
** **
&#This looks very good. Let me know if you have any questions. &#
&#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
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#