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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).
• What is the clock time at the midpoint of this interval?
The clock time at the midpoint would be 9 sec. This is derived by subtracting 5 from 13 resulting in 8 sec. 8 sec is the total duration of time and half of that time is 4 sec. The midpoint is at 5 sec plus half the duration of time (4 sec) which results in 9 sec.
answer/question/discussion:
• What is the velocity at the midpoint of this interval?
The velocity at the midpoint would be 28 cm/s. This is derived by subtracting 16cm/s from 40 cm/s resulting in 24 cm/s. 24cm/s the total change in velocity and half of that velocity is 12cm/s. The midpoint is at 16cm/s plus half the total change in velocity (12 cm/s) which results in 28 cm/s.
answer/question/discussion:
• How far do you think the object travels during this interval?
I think the object travels 192 cm. This answer is derived by multiplying the change in time by the change in velocity. 8 sec * 24 cm/s = 192 cm.
answer/question/discussion:
• By how much does the clock time change during this interval?
The clock changes by 8 sec. This is derived by subtracting 5 sec from 13 sec resulting in 8 sec.
answer/question/discussion:
• By how much does velocity change during this interval?
The velocity changes by an average of 24 cm/s. This is derived by subtracting 16cm/s from 40cm/s resulting in 24 cm/s.
Careful of terminology, which can trip you up. The velocity changes by 24 cm/s, not by an average of 24 cm/s.
answer/question/discussion:
• What is the rise of the graph between these points?
Rise is the 8 sec or the time duration.
answer/question/discussion:
• What is the run of the graph between these points?
The run is 24 cm/s or the velocity.
answer/question/discussion:
• What is the slope of the graph between these points?
The slope is rise over run. 8s/ (24cm/s)
answer/question/discussion:
• What does the slope of the graph tell you about the motion of the object during this interval?
I think that it proves that the object is accelerating.
answer/question/discussion:
• What is the average rate of change of the object's velocity with respect to clock time during this interval?
I think that it shows that the object increases in velocity at an average of 3 cm/s. Based on the formula used in determining the slope.
Good, but that would be 3 cm/s^2. Always do the algebra of the units.
answer/question/discussion:
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15 min
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&#Good responses. See my notes and let me know if you have questions. &#