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course Phy 231
6/6/2011 @ 2247
Problem 1If the velocity of the object changes from 4 cm / sec to 16 cm / sec in 8 seconds, then at what average rate is the velocity changing?
There is a change of rate of 12cm/sec over 8 seconds for and average change in rate of 1.5 cm/sec. (12/8)=1.5
A ball rolling from rest down a constant incline requires 8.2 seconds to roll the 97 centimeter length of the incline.
• What is its average velocity?
97 cm / 8.2 sec = 11.8 cm/sec.
An object which accelerates uniformly from rest will attain a final velocity which is double its average velocity.
• What therefore is the final velocity of this ball?
If an object is accelerating uniformly at 2 m/s then the final velocity is 4 m/s.
• What average rate is the velocity of the ball therefore changing?
The average velocity is 2 m/s.
@& The ball's average velocity is 11.8 m/s.
2 m/s would not be a rate of change of velocity. The units aren't right, and nothing in the given information implies 2 m/s or 2 m/s^2.
If the ball starts from rest and averages 11.8 m/s, its final velocity is not 4 m/s.
If the ball starts at 0 cm/s and averages 11.8 cm/s, what must be its final velocity, assuming a straight-line v vs. t graph?
What is the definition of average velocity? What is the definition of average acceleraiton? How can these definitions be applied to this situation?
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An automobile accelerates uniformly down a constant incline, starting from rest. It requires 10 seconds to cover a distance of 132 meters. At what average rate is the velocity of the automobile therefore changing?
132 meters / 10 seconds = 13.2 m/s (average velocity)
@& This is the average velocity.
The question asked for the average acceleraiton.*@
Problem 2
For a certain pendulum, periods of T = .91, 1.291681, 1.58539 and 1.83345 seconds are observed for respective lengths L = 7, 14, 21 and 28 units.
• Determine whether the transformation T -> T2 or T -> T3 linearizes the function better.
The function did not appear to get any more linear with the transformations.
• Determine the equation of the resulting straight line, and solve the equation for T.
The equation of a straight line is y = mx + b and in case m = 0.0544 and b = 0.5292. When you solve for T you get T = mx + b
• Use your equation to determine the period of a pendulum whose length is 51.19815 units.
T = (0.0544) * (51.19815) + (0.5292) = 3.31437 sec
• Use your equation to determine the length of a pendulum whose period is 2.424873 seconds.
(2.424873) = (0.0544) * (x) + (0.5292) = 34.84693 units
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@& Good work on the second problem.
You didn't get the first series of questions. See my notes. This is a very fundamental situation and you need to be able to reason it out.
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