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.
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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: ->->->->->->->->->->->-> (start in the next line):
Quantity A is the distance in cm, and quantity B is the time in seconds. Average rate of change= 10cm/5 seconds= 2cm/s
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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):
Quantity A is distance and B is time. (40cm-10cm)/3seconds= 10cm/s
distance is not one of the quantities involved in this rate
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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):
We know the rate of change is 5cm/second= Quantity A (distance)/ 10 seconds, so 5cm/s *10= 50cm which is quantity A. The position changes by 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):
The rate of change of an object is the distance an object travels divided by the time it takes that object to reach the distance. Once you have two variables it is possible to solve for A, B or the rate of change.
rate does not necessarily involve distance or clock time
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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):
When given a rate of change question, I will first look to see what the question is asking me. If it wants to know the rate, then I should be given the distance and time in the problem. I could then find the change in the distance and divide that by the change in time. This would give me the rate of change. I f I was only given either quantity A or B then the rate would be given and I could multiply the rate by which ever quantity was given in order to find the missing information.
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15 min
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&#Please compare your solutions with the expanded discussion at the link
Solution
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