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Phy 241
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):
Change in position is 10cm and change in time is 5 seconds. The rate of change in position with respect to time is 10cm / 5s = 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):
The speed changes by 30cm/s over the 3 second period. The average rate of change in speed over the time period is 30cm/s / 3s = 10cm/s^2. ????If I write in the units and multiply them through as we normally do, I wind up with s^2, is this correct? It has been a while since I have worked with units in detail and am not sure if that is right????
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All your reasoning is correct, as is your calculation of the units. Very good.
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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):
Since position changes by 5cm/s over a period of 10s, the position changes by 5cm/s * 10s = 50cm.
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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 easiest way for me to remember this is to look at the units. If I am given a measurement of distance and a period of time and am told to find the rate of change in distance over time. I can find this by using change in distance/amount of time passed.
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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):
Again, the best way is by looking at the units. If you need cm, and are given cm/s and s, you use cm/s * s = cm to get the distance measurement.
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Very good. Units are a good guide. If the units don't work out right, you've got an error either in your units calculation or in the process of your solution.
It's important to remember that incorrect reasoning can sometimes lead to correct units, so reasoning by units is not infallible. But it's very useful.
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&#Your work looks good. See my notes. Let me know if you have any questions. &#