Phy 121
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: ->->->->->->->->->->->-> :
The change in cm is: 20 cm- 10 cm= 10 cm. The change is time is: 9 sec- 4 sec= 5 sec. The average rate of change is cm/ sec.
10 cm/5 sec= 2 cm/sec
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: ->->->->->->->->->->->-> :
The change in velocity is: 40 cm/sec- 10 cm/sec= 30 cm/sec. The change in time is 3 seconds.
The change of velocity with respect to time is:
(30 cm/sec)/ (3 sec)= 10 cm/sec^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: ->->->->->->->->->->->-> :
To find how much the distance changes when the time changes by 10 seconds, we can multiply the average rate of position by the change in time:
5 cm/sec*10 sec= 50 cm. The position changes by 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: ->->->->->->->->->->->-> :
I will remember the definition simply as A/B. I will also remember the notation / as with respect to. Therefore I will remember the definition as A with respect to B.
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: ->->->->->->->->->->->-> :
If the question asks you to find the average rate of change for something (i.e. A) with respect to something else (i.e B), you subtract the two given A variables and divide them by the difference in the B variables. I will remember to apply this procedure by always assigning letters to the recognized variables and then plugging them into A/B.
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35 minutes
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&#Very good responses. Let me know if you have questions. &#