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course Phy231
I recommend that work these questions before the last minute. Your brain adapts better if you spread your thinking out.I also recommend that you submit them when they are complete, rather than waiting until the last minute. This is so you can get my feedback on one thing before you move to another.
In any case, the last minute will be 6:00 p.m. next Tuesday.
Note that this deadline (as well as the advice to spread things out) also applies to your other assignments. There is no need to get them in by Sunday night since we don't have class on Labor Day.
If you have questions, use the Question Form at
http://vhcc2.vhcc.edu/dsmith/forms/question_form.htm .
Give your counts for the four observations made today, in the order you made them:
First: 10
Second: 12
Third: 14
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According to your counts, which way did the table slope, to the right or left as it appeared on your screen?
I don’t remember which way it was slanted
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You will need to know this definition, word for word and symbol for symbol, starting now and for the rest of the course. The definition is about 19 words and a few symbols long and most of the words are single syllables:
Definition of average rate of change: The average rate of change of A with respect to B is (change in A) / (change in B).
You should already recognize this definition as perhaps the most fundamental definition in calculus, though it could be asserted that the most fundamental definition also applies a limiting process to this definition.
You also need the following two definitions:
Average velocity is the average rate of change of position with respect to clock time.
Average acceleration is the average rate of change of velocity with respect to clock time.
According to the definition of average rate of change, then, what is the calculation for velocity?
V=distance/time or change in position/time
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distance and change in position are two different things.
the denominator is not time.
Not bad, but you need to interpret the definition strictly and correctly.
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Explain how this calculation is consistent with your experience.
Finding the miles per hour which is a cars velocity you can take the number of miles traveled in a certain amount of time and divide one by the other. Usually it is miles and hours
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Explain how this calculation is consistent with formulas you've learned.
It’s an average rate so taking the averages of the other formulas you can get an estimate of how fast an object is going
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Specifically apply this definition to find the average velocity of the ball in each trial, assuming it traveled 60 cm during each interval of observation.
First trial: 60/10= 6.0 cm per count
Second trial: 60/12= 5.0 cm per count
Third trial: 60/14= 4.3 cm per count approximately
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Now this is where things start to get a little tricky. You should answer the following with the best of your common sense, thinking about what the questions mean rather than looking up formulas and explanations. The answers should come from you, not from some other source. And you should do your best to answer the questions without talking to your classmates, though once you have done your own thinking it would be great for you to discuss it with whomever you can.
You know the ball started from rest in each trial, as some of you stated in class today. You've just calculated the average velocities for the four trials.
Knowing that the ball starts from rest and knowing its average velocity, using only common sense and not some formula that might give you the right answer without requiring you to understand anything, explain the most reasonable approach you can think of to finding the final velocity.
Well knowing how to find the velocity of a car by using the miles and hours thinking I would have counted in seconds how many centimeters were traveled in the amount of time.
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That gives us the average velocity.
We need to know the final velocity for this situation.
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Assuming you do know the final velocity and the count, how would you apply the definition of average rate of change and the definition of average acceleration to determine the acceleration of the ball?
Knowing the average velocity of each trial you could take that answer and divide by the time to get the average acceleration.
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How does the definition tell you average acceleration must be calculated?
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Using your best estimate of the ball's final velocity for each of the four trials, what is the average acceleration for each? Show in detail how you get the average acceleration for the first trial, then just include the brief details of your calculation for each of the other three trials.
First trial: 6.0/10= 0.6
Second trial: 5.0/12= 0.42
Third trial: 4.3/14= 0.31
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It appears that you have divided your average velocities by the changes in clock time.
Note first that these quantities all have units, and that units must be used throughout your calculations.
Note next that you calculation does not follow from the definitions.
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By what percent do you estimate the average frequency of your counts might have varied between trials? Express your answer as the difference between the lowest and highest frequency, as a percent of the average of all the frequencies. Don't go looking up a technical definition of the word ""frequency"", which would probably confuse the whole issue. You have enough intuition about the meaning of that word to come up with a reasonable, if not profoundly accurate, estimate. You also shouldn't have to look up what we mean by the difference between the frequencies as a percent of the average frequency, but that terminology is well-defined, completely applicable and should not be confusing so if you've got to look it up it's OK.
I have no idea. My counts could have varied a little since there was a break in between each round and the counter could have gotten off. I was tapping out the rhythm on the table with my fingers but I could still have gotten off.
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By how much do you think you were off?
Were you at some times tapping twice as fast at at others?
Or do you think you managed to keep it within, say, 10% (or better)?
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If the frequency for a trial was off by 2%, by what percent would the resulting calculation of velocity be off?
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If the frequency for a trial was off by 2%, by what percent would the resulting calculation of acceleration be off?
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"
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A number of question need to be revisited and you need to apply the definitions more precisely, but you've done some good things here.
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