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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.
** CQ_1_02.2_labelMessages **
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):
The clock time is at 9 seconds. Change in t is 9 seconds. Either add half of 8 to 5 or subtract half of 8 from 13.
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Good. Another alternative is to find the mean of 5 and 13.
In any case, as you clearly understand, the mean is halfway between the two numbers.
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What is the velocity at the midpoint of this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
40 - 16 = 24 / 2 = 12 + 16 = 28 cm/s
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How far do you think the object travels during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
It traveled approximately 12cm.
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The interval lasts for 8 seconds, and the minimum velocity is 16 cm/s. So it travels a lot further than 12 cm.
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By how much does the clock time change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
Clock time changes by 4 seconds, which is halfway between 5 and 13 seconds, or 9 seconds at the midpoint.
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If the clock runs from 5 seconds to 13 seconds, it changes by 8 seconds.
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By how much does velocity change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
The velocity is 12cm/4sec = 3cm/sec
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12 cm is your result for the distance. If 4 sec was the duration of the interval, then 3 cm/s would be the average velocity on the interval.
This isn't the change in velocity.
What was the velocity at the beginning of the interval?
What was the velocity at the end of the interval?
By how much did velocity therefore change?
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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):
40cm/sec - 16cm/sec = 24cm/sec = change in velocity
13 sec - 5 sec = 8 sec = change in clock time
24cm/sec / 8sec = 3cm/s^2
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This is correct. Very good.
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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 40cm/sec - 16cm/sec = 24cm/sec = change in velocity.
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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 13 sec - 5 sec = 8 sec = change in clock time.
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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 equal to the average rate of change of velocity with respect to clock time on this interval, which is 3.
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The slope has units, which as you showed earlier are cm/s^2.
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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):
It tells me that the motion of the object during this interval changes at a rate of 3cm per second per second.
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Good.
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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):
A little confused here. Did we change intervals? Is this the same as above? 40cm/sec - 16cm/sec = 24cm/sec = change in velocity
13 sec - 5 sec = 8 sec = change in clock time
24cm/sec / 8sec = 3cm/s^2
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You have a couple of errors, but at the end you got good results, so I believe you pretty much understand what's going on here.
&#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. &#
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