Phy 201
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: **************** Quantity A is the ball that is rolling along the track. Quantity B is the time in seconds on the clock. The change in quantity A is 10 cm, where it’s position changed from 10 cm to 20 cm. The change in quantity B is 5 seconds, where the time went from 4 seconds to 9 seconds. The average rate of change in this problem would be 2 cm per second. You find this by dividing the change in quantity A (10 cm) / the change in quantity B (5 seconds) which gives you an average rate of change of 2 cm per second.
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: **************** Quantity A is the velocity of the ball rolling along the track. Quantity B is the clock time. The change in quantity A is 30 cm. The change in quantity B is 3 seconds. In order to find the average rate of change you must divide the change in quantity A by the change in quantity B, which is 30 cm per second/ 3 seconds and this gives you the average rate of change of 10 cm per second.
You have an error in your units.
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: **************** The position will change by 50 cm. You multiply the change in clock time which is 10 seconds by the distance in which the position changes with respect to clock time which is 5 cm/ second and that gives you 50 cm.
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: **************** I will read and re-read the definition and also write it down in my notes several times and then apply my knowledge of the definition through practicing examples.
You are asked in this exercise to apply the definition, and give 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: **************** When you are trying to find the average rate of change in a given quantity the ratio will always be the average rate of change in A in respect to the change in B. For instance, if you were to observe a boat floating down a river and its position changes from 10 meters to 70 meters in the time that you are observing it, and the time it take the boat to travel changes from 1 second to 7 seconds, the average rate of change can be determined to be 10 meters per second. This can be calculated by dividing the change in quantity A which is the position of the boat by the change in quantity B which is the time in which is the time in seconds and this gives you 60 m / 6 seconds which ultimately yields the average rate of change that is 10 meters per second.
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20 minutes
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You're doing a good job of applying the definition of rate of change. Your only error is with the units of one calculation (see my note).
&#At least part of your solution does not agree with the solution and comments given at the link below. You should view the solution at that link and self-critique as indicated there.
Solution
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