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course Phy 121
Rand Prob asst 02#$&*
course Phy 121
If 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?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?
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?
• What average rate is the velocity of the ball therefore changing?
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?
The velocity is changing at a rate of 12cm/sec / 8 sec = 1.5m/s^2
The vAve = 97cm/8.2sec = 11.8 cm/sec. So the object will average moving 11.8cm per second over the 97cm.
The final velocity of this ball is 11.8cm/sec *2 = 23.6cm/sec
The average rate the velocity is changing is 23.6cm/sec / 8.2sec = 2.9cm/sec^2, so it's changing at a rate of 2.9cm/sec per second(unit change in x).
vAve = 132m / 10sec = 13.2 m/s / 10 sec = 1.32 m/s^2, or the rate at which the velocity is changing over 132 meters is 1.32 m/s per second(unit change in x).
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&&&&&&&& Ah, got it. vAve = 132m/10sec = 13.2m/s, and, 13.2m/s / 10sec = 1.32m/s^2, or the rate at which the velocity is changing over 132 meters is 1.32m/s per second(unit change in x).&&&&&&&&&&
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However the rate of change of velocity is not ave velocity / change in clock time, it's change in velocity / change in clock time.
What is the initial velocity during this 10-second interval?
What is the final velocity during this interval?
What therefore is the change in velocity?
Now what is the average rate of change of velocity with respect to clock time?
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It's not so that
132m / 10sec = 13.2 m/s / 10 sec = 1.32 m/s^2
This would imply, among other things, that 132 m / (10 s) = 1.32 m/s^2
Avoid using the = sign for train-of-thought. The = sign has a very specific meaning that shouldn't be confused.
You could say that
132m / 10sec = 13.2 m/s
and
13.2 m/s / 10 sec = 1.32 m/s^2
(though I would recommend using parentheses around the denominator to avoid confusion with order of operations).
However this would not correctly answer the given question.
The average rate of change of velocity with respect to clock time is (change in velocity) / (change in clock time), which is a very important quantity.
Your calculation is (average velocity) / (change in clock time). In addition to not answering the question correctly, average velocity / change in clock time has no significant meaning.
At this point of the course, this is a very common error. It's rare that a student doesn't make it at least once.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes.
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Good, but you still need to make one correction.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes. &#
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