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: ->->->->->->->->->->->-> :
To solve for this we subtract the beginning time from the ending time:
13 sec- 5 sec= 8 sec, divide that by two which equals for and then add that to the starting time:
Midpoint= 9 sec
• What is the velocity at the midpoint of this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
40 cm/sec- 16 cm/sec= 24 cm/sec, divide that by 2 which gives us 12 and then add that to the starting velocity:
16+12= 28 cm/sec
• How far do you think the object travels during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
Because the average velocity is 24 cm/sec, we multiply it by the average time of 8 sec to find the distance:
24 cm/sec* 8 sec= 192 cm
• By how much does the clock time change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
13 sec- 5 sec= 8 sec
• By how much does velocity change during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
40 cm/sec- 16 cm/sec= 24 cm/sec
• What is the average rate of change of velocity with respect to clock time on this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
24 cm/sec/ 8 sec= 3 cm/sec/sec
• What is the rise of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> :
40 cm/sec- 16 cm/sec= 24 cm/sec
• What is the run of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> :
13 sec- 5 sec= 8 sec
• What is the slope of the graph between these points?
answer/question/discussion: ->->->->->->->->->->->-> :
24 cm/sec/ 8 sec= 3
• What does the slope of the graph tell you about the motion of the object during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
The object is decreasing in velocity as clock time increases.
• What is the average rate of change of the object's velocity with respect to clock time during this interval?
answer/question/discussion: ->->->->->->->->->->->-> :
24 cm/sec/8 sec= 3 cm/sec/sec
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20 minutes
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Solution
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