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):
The clock time would be 9 seconds.
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What is the velocity at the midpoint of this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
First I found the change in the speed, 40 - 16 = 24 so 24 cm/s is the amount the speed changed over the interval, the interval was 8 seconds long so I divided the 24 / 8 = 3, so it was changing at a rate of 3 cm/s/s. With that information and knowing the midpoint to be 9 s, which is 4 more than the start point, 4*3 = 12 cm/s, knowing the starting speed was 16 cm/s after adding those two you get 28 cm/s.
Good reasoning.
Note that you would have obtained the same result by averaging the 16 cm/s and 40 cm/s initial and final velocities.
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How far do you think the object travels during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
By averaging the two speeds we can determine an average speed over the whole interval, 16 + 40 = 56, 56 / 2 = 28, so 28 cm/s is the average velocity. The interval is 8 seconds long so 28 * 8 = 224, so it travelled 224 cm.
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By how much does the clock time change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
The interval is 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 changed by 24 cm/s.
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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):
The avg. rate of change of velocity was 3 cm/s/s.
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What is the rise of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
24 cm/s.
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What is the run of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
8 seconds.
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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.
The slope has units, which you can easily verify to be 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):
The slope is also the average rate of change of velocity.
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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):
3 cm/s/s.
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25 minutes
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&#Good responses. See my notes and let me know if you have questions. &#