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course Phy 121
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):
Since the ball rolling rolls from 10 cm to 20 cm, it has a change of 10 cm. The clock changes from 4 seconds to 9 seconds, giving it a change of 5 seconds. The problem you have here would be: (10cm)/(5 sec)= 2cm/sec
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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):
With the balls velocity change, 30 cm/sec, and the clock’s change, 3 seconds, we get the following formula: (30cm/sec)/(3sec)= 10cm
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30 cm/s / (3 s) = 10 (cm/s) / s = 10 (cm/s) * (1/s) = 10 cm/s^2, not 10 cm.
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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 we are given the average rate, we have to solve for the rate of change of distance. This is done like this:
(change of A)/(10sec)= 5cm/sec
Change of A= 5cm/sec(10sec)
Change of A= 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):
Rate of Change of one quantity with respect to another = Change of A / Change of 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):
You will either be given two different rates and how they are changed, and will solve the problem by plugging in those changes, or you will be given the final rate of change and be expected to solve for either change of a or change of b.
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Very good, but you made one error on the units. Check my note.
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