class_notes3questions_060131

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18:22:47 Given the initial velocity, final velocity and time duration of a uniformly accelerating object, how do we reason out the corresponding acceleration and change in the position of an object?

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RESPONSE --> If you have the initial velocity and the final velocity and the time interval you can first find the average velocity. The average velocity is the final velocity minus the initial velocity which is all divided by the time interval. This then gives you the average vleocity 'ds/'dt.. To find the acceleration you take the final velocity which would be the change in velocity because you started from rest and then divide it by the time interval. The acceleration is cm/s/s

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18:25:04 ** COMMON ERRONEOUS STUDENT RESPONSE: To find the average acceleration, we divide the change in veolocity by the time interval. To find the change in position or displacement of the object over any time interval multiply the average velocity over that interval by the duration of the interval. You are not given the average velocity or the change in velocity. You have to first determine the average velocity; then your strategy will work. Since acceleration is constant you can say that average velocity is the average of initial and final velocities: vAve = (v0 + vf) / 2. Change in velocity is `dv = vf - v0. Now we can do as you say: To find the change in position or displacement of the object over any time interval multiply the average velocity over that interval by the duration of the interval. **

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RESPONSE --> That is what I said that you should do is determine the average velocity.

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18:28:41 In terms of the meanings of altitudes, area, slope and width, how does a velocity vs. clock time trapezoid represent change in position and acceleration?

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RESPONSE --> By finding the area under the trapezoid you can find the slope of the line which is the acceleration. The slope is rise over run which is the change in velocity by the change in time.Which is the aceceleration.

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18:30:44 ** If you multiply the average altitude by the width (finding the area) of the trapezoid you are multiplying the average velocity by the time interval. This gives you the displacement during the time interval. The rise of the triangle represents the change in velocity and the run represents the time interval, so slope = rise / run represents change in velocity / time interval = acceleration. **

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RESPONSE --> that is true that you would get the change in position by finding the area of the trapezoid. Since rise is velocity=displacement/time and you then divided it by time which is actually multiplying it by 1/time then only thing left woud be the displacement.

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Good statements. Let me know if you have questions.