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: ->->->->->->->->->->->->
A = change in distance
B = change in time
(20cm-10cm)/(9sec-4sec) = 10cm/5sec = 2cm/sec
the average rate of change with distance related to time is 2cm/sec
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: ->->->->->->->->->->->->
A = rate of change of velocity (cm/sec)
B = clock time change
(40cm/sec 10cm/sec)/3 sec = (30cm/sec)/3 sec = 10cm/sec
the average rate of change of velocity = 10cm/sec
`er11
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: ->->->->->->->->->->->->
A = change of position
B = change in time
(5cm/sec)(10sec) = 50cm
you multiply these because you are trying to find the average rate of change with respect to A instead of B. Therefore, you have to change the equation around
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 feel like I will be able to remember this definition because any time you have a change in anything, lets use A for example. Change in A is always going to have to be something else divided by A. Whatever you are using, lets use C, is going to be divided by A to show a change with respect to A.
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: ->->->->->->->->->->->->
You first must recognize what is your A and what is B. Once you have identified A and B, you them must decide what is going to be in the denominator and what is going to be in the numerator, or if you are going to change the equation around and multiply your two values. Generally the problem will tell you to find something in respect to something else. That is how you know what to designate as A and B and then you, remembering the formula, plug in the values that you have designated.
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15 minutes
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&#Please compare your solutions with the expanded discussion at the link
Solution
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