Phy 231
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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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).
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What is the clock time at the midpoint of this interval?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
(5 + 13 sec)/2 = 9 seconds.
The clock time at the midpoint would be 9 seconds.
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What is the velocity at the midpoint of this interval?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
(40 cm/s - 16 cm/s)/(13 sec - 5 sec) = 3
this quantity has units, which should be specified
y = 3x + b
16 = 3(5) + b
b = 1
y = 3x + 1
so @ 9 sec
y = 3(9) + 1
y = 28 cm/sec
good use of the function, though since it's linear a simple average would have also worked
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How far do you think the object travels during this interval?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
well, since average velocity according to the two points is (40 cm/sec + 16 cm/sec)/2 = 28 cm/sec and the interval lasts (13 sec - 5 sec) = 8 sec
and (28 cm/sec)* 8 sec = 224 cm.
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By how much does the clock time change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
It changes 13 sec - 5 sec = 8 sec
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By how much does velocity change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
It changes 40 cm/sec - 16 cm/sec = 24 cm/sec
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What is the average rate of change of velocity with respect to clock time on this interval?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
(24 cm/sec)/8 sec = 3 cm/sec^2 would be the average rate of change of velocity
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What is the rise of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
Well, since 40 cm/s - 16 cm/s = 24 cm/sec, it would be 24 cm/sec between the points.
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What is the run of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
Well, since 13 s - 5 s = 8 sec, it would be 8 sec.
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What is the slope of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
The slope would be 3, since 24/8 is 3. Also, I can look at my equation above and see from the 3x that the slope is 3.
be sure to always specify 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: ->->->->->->->->->->->-> scussion: That the velocity of the object is increasing at an increasing rate.
position increases at an increasing rate; velocity increases at a constant rate
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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: ->->->->->->->->->->->-> scussion:
(24 cm/sec)/8 sec = 3 cm/sec^2 would be the average rate of change of velocity with respect to clock time.
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10 minutes
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Solution
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