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phy121
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.
** CQ_1_01.1_labelMessages **
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 is the position change and quantity B is the change in the time in seconds
(20-10)/(9-4) gives 10/5 = 2 cm /second.
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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):
qty a is the change in velocity
qty b is the change in clock time
so (40-10)/3 = 30cm/sec/3 sec so the answer would be 10 cm per second squared.
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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):
the average rate of change of a with respect to b is found by change a/change b
we are given the rate at which position changes with respect to clock time
so that means that qty a is the position change and qty b is the clock time
so 5cm/sec = position change / 10sec
solving we get that the position change would be equal to 50 cm.
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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):
I will remember this definition as the rate of change in quantity A with respect to quantity B is found by the formula change in A/change in B
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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):
if I am given a problem to apply this definition to I will remember that the rate of change in quantity A with respect to quantity B is change in A/change in B so the first step is to make sure that you label quantity A and quantity B correctly based on the definition and then you find the change in quantity A and divide it by the change in quantity B.
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Excellent.
Once more the connections to the derivative (rate of change) and integral (change in quantity) are not required might provide you with an even surer grasp of these concepts.
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