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Phy 121
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.
** CQ_1_01.1_labelMessages **
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):
average rate of change of its position with respect to clock time = vAve = ‘ds / ‘dt
vAve = (20 cm - 10 cm) / 9 s = 10 cm / 9 s = 1.11 cm/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):
average rate of change of its velocity with respect to clock time = aAve = ‘dv / ‘dt
aAve = (40cm/s - 10cm/s) / 3s = 30cm/s / 3s = 10 cm/s^2
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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):
‘ds = vAve * ‘dt
‘ds = 5cm/s * 10s
‘ds = 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):
I will ensure that I remember this definition by memorizing it word for word and actually understanding what it means.
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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):
I will think back to the basic definition, average rate of change of A with respect to B = (change in A) / (change in B) in order to apply it to situations where quantity A and quantity B are given. For example, average rate of change of position with respect to clock time is the definition for average velocity where position is quantity A and clock time is quantity B.
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&#Very good work. Let me know if you have questions. &#
Compare acceleration results for the two different methods
You obtained data for three basic setups, each with a different slope. Each basic setup was done with a right-left and a left-right version.
• You previously calculated a single average rate of change of velocity with respect to clock time for each slope, by averaging the right-left rate with the left-right rate.
• You have now calculated a single average rate of change of velocity with respect to clock time for each slope, but this time by using the average of the mean times for the right-left and left-right versions.
Answer the following questions in the box below:
Since both methods give a single average rate of change of velocity with respect to clock time, would you therefore expect these two results to be the same for each slope?
Are the results you reported here, based on the average of the two mean times, the same as those you obtained previously by average the two rates? Are they nearly the same?
Why would you expect that they would be the same or nearly the same?
If they are not exactly the same, can you explain why?
------>>>>>> ave of mean vel, ave based on mean of `dt same, different, why
Your answer (start in the next line):
The changes in average velocity and acceleration seem to correspond with each other in that they both increase as more dominoes are added to the slope. The average velocity and acceleration are not going to be exactly the same, given the minute but still prevalent human error, but they will be close to each other.
:
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