#$&*
course Phys201
6/12 @9:55pm
RandomProb2-1#$&*
course Phys201
6/10 @7:42pm
If the velocity of the object changes from 3 cm / sec to 13 cm / sec in 7 seconds, then at what average rate is the velocity changing?vAve=`ds/`dt
vAve=13-3/7
vAve=10/7
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`` You need to use units throughout your calculation, and actually do the algebra of the units.
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vAve=1.43 cm/sec
&&&& vAve=13cm/sec-3cm/sec/7 sec=1.43 cm/sec=sig digits= 1 cm/sec
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You do need to use signs of grouping for that numerator. That is necessary in any case, but it also might help you understand the units calculation.
(13cm/sec-3cm/sec) / (7 sec) =
10 cm/sec / (7 sec) =
1.43 (cm/sec) / (sec).
(cm/sec) / (sec) is not the same as cm/sec.
You need to do the algebra of the units.
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A ball rolling from rest down a constant incline requires 9.6 seconds to roll the 99 centimeter length of the incline.
• What is its average velocity?
vAve=`ds/`dt
=99cm/9.6sec
=10.3 cm/sec
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This calculation is done correctly.
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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?
vf=0
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The ball has average velocity 10.3 cm/s.
An object which accelerates uniformly from rest will attain a final velocity which is double its average velocity.
It does not follow that vf = 0.
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The average rate is not changing. We know this because the problem states that the object accelerates uniformly.
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&&&& vAve=10.3 cm/s, vf=10.3*2=20.6 cm/s
The average rate of change of the ball's velocity is not zero.
That means that the velocity of the ball is changing. If it wasn't, then this average rate of change would be zero.
Uniform acceleration means that the rate of change of the velocity is not changing, so the rate is always equal to the average rate.
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&&&& Average rate=rate, so rate=10.3 cm/s
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10.3 cm/s is the average velocity, which is the average rate of change of position with respect to clock time.
There is more than one average rate involved here.
You are asked not for the average velocity, but for the average rate at which velocity is changing with respect to clock time.
What is the definition of the average rate of change of velocity with respect to clock time?
What is the initial velocity for this interval?
What is the final velocity for this interval?
What is the change in velocity for this interval?
What is the change in clock time?
What therefore is the requested average rate?
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An automobile accelerates uniformly down a constant incline, starting from rest. It requires 16 seconds to cover a distance of 120 meters. At what average rate is the velocity of the automobile therefore changing?
vAve=`ds/`dt
dt=16 sec
ds=120m
vAve=120/16
&&&& vAve=`ds/`dt=120m/16 sec, vAve=7.5 m/sec
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`` You need to use units throughout your calculation, and actually do the algebra of the units.
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vAve=7.5m/s
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You have found the autmobile's average velocity.
You have yet not found the average rate of change of its velocity with respect to clock time, which is what was requested.
The preceding series of questions shows you how to reason this out.
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&&&& rate=vAve which is 7.5m/sec
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This is an average rate, but it's not the average rate that was requested.
Once more, the previous problem works out how to find the average rate of change of velocity with respect to clock time, which is the average rate requested by this problem.
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You are doing some good thinking, but as is commonly the case at this point you are making some errors.
I believe you'll be able to make corrections without too much trouble, based on the notes I've inserted.
&#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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"
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You don't seem to have noticed that there are two different average rates involved here.
One is the average rate of change of position with respect to clock time, which is the average velocity.
The other is the average rate of change of velocity with respect to clock time, which is also called acceleration.
You have given average velocities as answers to the question of the average rate of change of velocity.
I'll ask for another revision. This time use #### to denote your insertions.
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