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course Phy 201
September 8th around 2:45 pm
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):
(10cm) / (5seconds) = 2 cm per second
This answer was found by taking the change in A (the distance traveled) divided by the change in B (the time it took for the ball to travel).
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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):
(30cm) / (3seconds) = 10 cm / second
This answer was found by taking the change in A (30 cm, found by taking the difference from 10 to 40) and dividing that by the change in B (3 seconds).
@& 10 cm, 30 cm and 40 cm are not quantities associated with this interval.
10 cm/second and 40 cm/second are, and can be used to calculate the changein the velocity.
This won't affect the numerical part of your result, but will affect the units of the numerator of your calculations, and therefore the units of your result.*@
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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/sec) * (10) = 50 cm
To solve this problem, we first look at the facts given. We know that the position changes at a rate of 5cm per second. Therefore, to find the rate at which the position changes after 10 seconds, we multiply 5cm/second by 10 seconds. The position changes by 50 centimeters.
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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):
To ensure that I will remember this definition, I will refer back to this exercise if need be. But, by performing these problems, I have not only read about the definitions but also gotten a visual for how they apply to the problems.
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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):
First, I will look at the problem given and notice the facts already included. Then, I will use the definitions to connect the values with the changes in A and B and solve the problem.
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@& Your reasoning is good throughout, but you did make a fundamental error with units. Fortunately it should be quick and easy to correct.
Note also that this is a 'seed' question and should be submitted using the form for that specific question. Doing so ensures that the document is correctly identified, which is not always important but sometimes is.
&#Please see my notes and, unless my notes indicate that revision is optional, submit a copy of this document with revisions and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes.
If my notes indicate that revision is optional, use your own judgement as to whether a revision will benefit you. &#