Video 9 10

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17:08:25 Physics video clip 09 displacement for linear v vs. t graph: common sense, formula, area If we know the initial and final velocities over some time interval, and if the rate which velocity changes is constant, then how do we calculate the displacement over a the time interval?

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RESPONSE --> You would divide the difference between the initial velocity and final velocity by the time interval

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17:08:46 ** Displacement is the product of average velocity and time interval. Since acceleration is uniform average velocity is average of initial and final velocities. Displacement could therefore be calculated from the final and initial velocities => `ds =[(vf + v0)/2] * `dt. **

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RESPONSE --> Oh ok

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17:08:55 Physics video clip 10 continuing 09: calculation of area

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RESPONSE -->

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17:10:10 How do we use a graph of v vs. t to depict the calculation of the displacement over a time interval?

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RESPONSE --> It would be the bottom half of the graph where the right triangle on the bottom is

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17:10:23 ** Looking at the graph, we notice a trapezoid created by the slope line across the top, and an imaginary line drawn from the y value down to and perpendicular to the x axis. The area of this trapezoid represents the displacement or 'signed distance' the object travels. The displacement for any time interval can be found finding the average of the two 'altitudes' of the trapezoid, which represent initial and final velocities. Multiplying the average 'altitude' by the width is therefore equivalent to multiplying the approximate average velocity by the time interval, giving us the area of the trapezoid, which represents the approximate displacement. In the case where the graph is linear (which corresponds to uniform acceleration) the average of the two altitudes in fact represents the average velocity, and the result is the displacement, not the approximate displacement. **

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RESPONSE --> ok

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17:10:53 What aspect of the graph gives the displacement during the time interval?

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RESPONSE --> The trapezoid on the bottome half

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17:11:10 ** STUDENT ANSWER: It is the average of the two sides that are as high as 'y' in each case, multiplied by the width-units of 'x'. **

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RESPONSE --> I dont understand

Displacement is the area of the v vs. t trapezoid, which is the average altitude of the trapezoid multiplied by its width.

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You appear to understand this reasonably well, but as noted before you should provide more details in answers and self-critique. Let me know if you have questions.