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Phy 121
Your 'cq_1_02.2' 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:
A graph is constructed representing velocity vs. clock time for the interval between clock times t = 5 seconds and t = 13 seconds. The graph consists of a straight line from the point (5 sec, 16 cm/s) to the point (13 sec, 40 cm/s).
What is the clock time at the midpoint of this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
13+5= 18/2 = 6
@& These quantities have units, which should be included.
However the sequence of your reasoning is good.
Note that 18/2 = 9, not 6.*@
The clock time at the midpoint of the interval is 6 seconds.
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What is the velocity at the midpoint of this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
Average velocity = 40 cm/sec - 16 cm/sec / 6 sec
24/6 = 4 cm/sec
@& Your units are not correct. If you divide cm/s by s you don't get cm/s.
Other than the unit error, you have a correct calculation of the average rate of change of velocity with respect to clock time.
That's a good calculation, but the question asked for the midpoint velocity, which would be the average velocity. This is very different from the average rate of change of velocity ... *@
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How far do you think the object travels during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
The object should travel 24 cm during this interval.
@& That is how far it would travel if its average velocity was 4 cm/s.
However the velocity is never less than 16 cm/s, so 4 cm/s is clearly not the average velocity.*@
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By how much does the clock time change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
The clock time changes by about 18 seconds throughout this interval.
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By how much does velocity change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
??? Im not for sure how to find this. I have found the average velocity once, but I dont how to decide how much the velocity changes during this interval.
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What is the average rate of change of velocity with respect to clock time on this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
??? Since I dont understand how to figure the previous question out, I cant solve this one. I know that we use the formula rate of change for A with respect to B.
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What is the rise of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
The rise is 24 between the point (5, 16) and (13, 40).
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What is the run of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
The run is 8 between the points (5, 13) and (13, 40).
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What is the slope of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
The slope is 3 cm/sec between the points.
@& Right, except for the units.*@
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What does the slope of the graph tell you about the motion of the object during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
The motion of the object is increasing by 3 cm/sec.
@& Not bad, but see the link at the end for more complete wording.*@
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What is the average rate of change of the object's velocity with respect to clock time during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
rate of change of A with respect to B
4cm/ sec / 6 seconds = 0.667 cm/ sec^2
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It took about 30 minutes to complete.
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@& You're on the right track with the definitions and basic operations. A little more practice and you'll be fine on this.
*@
&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#