Phy 231
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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?
The midpoint would be at time t = 9s.
->->->->->->->->->->->-> answer/question/discussion:
• What is the velocity at the midpoint of this interval?
Based on the equation of the line found using the two points, the velocity at t = 9 would be 28m/s.
->->->->->->->->->->->-> answer/question/discussion:
• How far do you think the object travels during this interval?
The change in velocity from 5 seconds to 9 seconds is 28-16 = 12/4 = 3cm/s/s. If it starts at 16cm/s and increases at 3cm/s/s then to find the answer you'd have to add up the velocities. 16+19+22+25+28 = 110cm.
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• By how much does the clock time change during this interval?
The time changes 4 seconds in this interval. 9 - 5 = 4.
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• By how much does velocity change during this interval?
The velocity changes from 28cm/s to 16 cm/s which is 12 cm/s.
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• What is the average rate of change of velocity with respect to clock time on this interval?
The average rate of change of the velocity is 3cm/s/s as found in the question earlier.
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• What is the rise of the graph between these points?
The rise of the graph between the first point and the midpoint is 12. 28 - 16 = 12.
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• What is the run of the graph between these points?
The run is 4. 9 - 5 = 4.
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• What is the slope of the graph between these points?
The slope between the two points is the rise/run. 12/4 = 3. So the slope is 3.
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• What does the slope of the graph tell you about the motion of the object during this interval?
The slope tells us the rate of change in velocity which happens to be 3cm/s/s. This is also the acceleration. Since the slope is positive and constant, it tells us that the velocity is increasing and at a constant rate.
->->->->->->->->->->->-> answer/question/discussion:
• What is the average rate of change of the object's velocity with respect to clock time during this interval?
The average rate of change of the object is 3cm/s/s.
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30 min
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&#This looks good. Let me know if you have any questions. &#