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: ->->->->->->->->->->->-> :
change in A= 10 cm change in B=20 cm 10/20= 0.5 change in A= 4 seconds change in B= 9 seconds 4/9= 0.4 change in A= 0.5 change in B= 0.4 0.5/0.4= 1.25. The average rate of change of its position with respect to clock time during this interval is 1.25.
• 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: ->->->->->->->->->->->-> :
40 cm -10cm = 30 cm 30 cm/ 3 seconds= 10 cm/s The average rate of change of its velocity with respect to clock time during this interval is 10 cm/s.
Change in A= 10 cm Change in B= 40 seconds 10/40= 0.25 Change in A= 0.25 Change in B= 3 seconds
• 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: ->->->->->->->->->->->-> :
Change in A= 5 cm Change in B= 10 seconds 5cm/ 10 seconds= 0.5 cm/s The position changes by 0.5 cm/s.
• 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 this definition by memorizing it, and it will be easy for me to remember because I know that A always comes before B. Change in A/ Change in 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: ->->->->->->->->->->->-> :
We find the average rate of change by dividing Change in A/ Change in B. We divide the number of displacement, which is usually measured in some sort of units by the elapsed time. I will remember to apply this procedure by remembering that the unit of measurement goes on top and the time goes on the bottom when dividing.
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40 minutes
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&#Please compare your solutions with the expanded discussion at the link
Solution
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