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phy 121
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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):
midpoint = ((x1 + x2) / 2), (y1 + y2) / 2)
midpoint = ((5 + 13 ) / 2), (16 + 40) / 2)
Midpoint = (18 / 2 , 56 / 2)
Midpoint = (9, 28)
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):
at the midpoint the velocity would be change in distance / change in time
velocity = (40 cm/s - 16 cm/s) / ( 13 s - 9s)
40 cm/s and 16 cm/s are velocities, not distances or displacements
velocity = 24cm/s / 4 s
24 cm/s is the change in velocity; 4 s is half of the time interval over which the velocity changes. This doesn't give you a velocity, and the units of cm/s / s are not cm/s.
velocity = 6 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):
13 s - 5 s = 8 s
8 s / 6 cm/s = 1.33cm/s^2
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By how much does the clock time change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
13 s - 5 s = 8 s
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By how much does velocity change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
(40 cm/s - 16 cm/s) = 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):
ave rate = change in vel / change in time
ave rate = 24cm/s / 8s
ave rate = 3 cm/s^2
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What is the rise of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
rise = 40 - 16 = 24
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What is the run of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
run = 13 - 5 = 8
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What is the slope of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
slope = rise / run
slope = 24 / 8
slope = 3
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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 at and increasing rate. It is increasing 3 times between each point.
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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):
ave rate = change in vel / change in time
ave rate = 24cm/s / 8s
ave rate = 3 cm/s^2
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30min
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Solution
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