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: ->->->->->->->->->->->-> : Midway clock time = 9 s
• What is the velocity at the midpoint of this interval?
answer/question/discussion: ->->->->->->->->->->->-> : Slope = rise / run = 24 / 8 = 3; At clock time velocity will have increased 12 to 28 cm/s
• How far do you think the object travels during this interval?
answer/question/discussion: ->->->->->->->->->->->-> : 16 @ 5 s, 19 @ 6 s, 22 @ 7s, 25 @ 8s, 28 @ 9 s, 31 @ 10 s, 34 @ 11 s, 37 @ 12 s = total 212 cm
• By how much does the clock time change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> : Clock time changes by 13 – 5 s = 8 seconds
• By how much does velocity change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> : Velocity changes by 40 cm / s – 16 cm / s = 24 cm / s
• What is the average rate of change of velocity with respect to clock time on this interval?
answer/question/discussion: ->->->->->->->->->->->-> : Average rate of change of velocity with respect to clock time = 24 cm / s / 8 s = 3 cm / s^2
• What is the rise of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> : Rise of the graph = change in velocity = 24
• What is the run of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> : Run of the graph = change in clock time = 8
• What is the slope of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> : Slope of graph = rise / run = 24 / 8 = 3
• What does the slope of the graph tell you about the motion of the object during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
• What is the average rate of change of the object's velocity with respect to clock time during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
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15 minutes
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Good answers to most questions.
See the link below and be sure you understand everything. I'll leave the question of a revision up to you; it's probably not necessary, though.
&#Please compare your solutions with the expanded discussion at the link
Solution
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