phy 121
Your 'question form' 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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I had a question about Week 3, Quiz 1, Version 1.
When solving for situation 10 on the chart, we are provided with a, 'dt, and 'ds.
I came up with my values of the given information, but struggled to solve for all given information.
I was trying to solve it using direct reasoning and was able to determine the average velocity and change in velocity, but was having alot of trouble determining v0 and vf.
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I can't seem to figure out with direct reasoning how to obtain the values for vo and vf. It seems like you need to have to be able to solve for the other. Can you point me in the right direction to solve this???
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Consider the following question:
List 5 pairs of numbers, with each pair having an average value of 10.
#$&* To get you started, 7 and 13 have average value 10, as do 4 and 16.
Now, for each pair answer the question: If your two numbers are the initial and final velocity of an object in cm/s, what is the change in velocity?
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For example 7 and 13 would mean that initial and final velocities are 7 cm/s and 13 cm/s have a difference of 6 cm/s. The change in velocity would be 6 cm/s.
The pair 4 and 16 imply change in velocity of 12 cm/s.
Now consider the following:
The average of two numbers is 12 and the difference between them is 4. What are the two numbers?
Before reading on take a few minutes (no more than 5) and see if you can figure out the answer.
#$&* OK, it would be possible to do this by trial and error. You would probably come up with the 10 and 14 as your numbers.
Observe that 12 is right in the middle, between 10 and 14. 10 is 2 less than 12, and 14 is 2 more than 12.
Now consider the next question:
If we know the average velocity of an object to be 17 cm/s, and the change in velocity to be 5 cm/s, what are the initial and final velocity?
#$&* You might get this by trial and error, but it's probably better to go ahead and reason it out.
17 cm/s is halfway between the initial and final velocity, and the difference between initial and final velocity is 5 cm/s. So the initial velocity must be half the difference, or 2.5 cm/s, lower than the 17 cm/s middle value, and the final must be 2.5 cm/s higher than the middle value.
2.5 cm/s lower than 17 cm/s is 17 cm/s - 2.5 cm/s = 14.5 cm/s, and 2.5 cm higher than 17 cm/s is 19.5 cm/s.
In general if we know the average of two velocities and change in velocity, the initial velocity will be 'half the difference' on one side of the average and the final velocity will be 'half the difference' on the other side.
Generalizing this using symbols, if we know v_Ave and `dv, then v0 = v_Ave - 1/2 `dv, and vf = v_Ave + 1/2 `dv.
Let me know if this helps. Be sure to ask if it doesn't.