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: ->->->->->->->->->->->-> :
(13 sec + 5 sec) / 2 = 18 sec / 2 = 9 sec
The clock time at the midpoint of this interval is 9 seconds (t = 9 seconds)
• What is the velocity at the midpoint of this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
(40 cm/s + 16 cm/s) / 2 = (56 cm/s) / 2 = 28 cm/s
The velocity at the midpoint of this interval is 28 cm/s
• How far do you think the object travels during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
The object travels between 16 cm and 40 cm, so it travels 24 cm during this interval.
• By how much does the clock time change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
13 sec – 5 sec = 8 sec
The clock time changes by 8 sec during this interval.
• By how much does velocity change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
40 cm/s – 16 cm/s = 24 cm/s
The velocity changes by 24 cm/s
• What is the average rate of change of velocity with respect to clock time on this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
`dv = rate of `dv * `dt
(24 cm/s) = rate of `dv * (8 s)
(24 cm/s) / (8 s) = rate of `dv
3 cm/s = rate of `dv
The average rate of change of velocity with respect to clock time on this interval is 3 cm/s.
• What is the rise of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> :
rise = (40 cm/s) – (16 cm/s) = 24 cm/s
• What is the run of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> :
run = (13 s) – (5 s) = 8 s
• What is the slope of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> :
slope = rise / run = (24 cm/s) / (8 s) = 3 cm/s
• What does the slope of the graph tell you about the motion of the object during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
The slope of the graph is a positive 3, which means that every time the y value increases by 3, the x value increases by 1. As y increases, x increases, and vice versa. The object is moving in a positive direction.
• What is the average rate of change of the object's velocity with respect to clock time during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
I think the slope is equal to the average rate of change of an object’s velocity which is 3 cm/s.
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15 minutes
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Good. A couple of minor errors, mostly with units, so check the link:
&#Please compare your solutions with the expanded discussion at the link
Solution
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