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course Phy 121
1/30 11
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):
20cm-10cm = 10cm
9s - 4s = 5s
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):
40cm/s - 10cm/s = 30cm/s
30cm/s / 3s = 10cm/s/s
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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):
5cm/s / 10s = .5cm/s/s
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You are dividing average rate of change of position with respect to time, by change in clock time. With fewer words you have divided average velocity by change in clock time.
An average rate divided by the change in clock time usually doesn't give you anything meaningful, and that is so in this case.
In this case you know that
ave rate = change in position / change in clock time.
If you know the ave rate and the change in clock time, then, you can find the change in position.
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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 right the definition down, and apply it until it is second nature.
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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 to changing quantities and asked for the rate of change, I will know to use this definition.
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&#Good responses. See my notes and let me know if you have questions. &#