Your 'cq_1_02.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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The problem:
A ball starts with velocity 4 cm/sec and ends with a velocity of 10 cm/sec.
What is your best guess about the ball's average velocity?
I believe the ball's average velocity is 7cm/sec. It started with 4cm/s and ended with 10cm/sec a difference of 6cm/sec. So if you subtracted 3 from 10 and added 3 to 4, you will get 7.
Without further information, why is this just a guess?
You don't know the distance that the ball is traveling, even though it started at 4cm/sec and ended at 10cm/sec doesn't mean it had an average velocity of 7cm/sec. It could have rolled on a straigh line then fell of an elevation, therefore speeding it up drastically at the end of its journey.
If it takes 3 seconds to get from the first velocity to the second, then what is your best guess about how far it traveled during that time?
Well, if I decided that it's travelign at an average speed of 7cm/s, I would have to answer that in 3 seconds it would have traveled 21cm.
At what average rate did its velocity change with respect to clock time during this interval?
I believe the average rate the velocity change with respect to clock time 2.33 cm/s.
I'm a little unclear on this one....do you divide average velocity by amount of time traveled?
The average rate of change of velocity with respect to clock time is not equal to the average velocity divided by the change in clock time.
Example: If we move for 2 hours at a constant velocity of 60 mph then our velocity doesn't change, so the average rate of change of velocity with respect to clock time would be 0. Our average velocity, however is 60 mph, and dividing average velocity by change in clock time would give us 60 mph / (2 hr) = 30 mph / hr. This clearly disagrees with the fact that in this situation the average rate of change of velocity with respect to clock time is zero, and demonstrates the vAve / `dt is not equal to the desired average rate. In fact, vAve / `dt is pretty much meaningless.
This is, of course, an easy error to make. Very easy to confuse vAve with `dv, and the only way to keep it straight is to think it through to be sure our calculation makes sense.
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20 min
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&#Good work. See my notes and let me know if you have questions. &#