Problem

Sound travels at a speed of about 344 $\mathrm{m}…

02:33

Problem 12 Easy Difficulty

A runner covers one lap of a circular track 40.0 $\mathrm{m}$ in diameter in 62.5 s. For that lap, what were her average speed and average velocity? (b) If she covered the first half-lap in 28.7 s, what were her average speed and average velocity for that half-lap?

Answer

a) 2.01 $\mathrm{m} / \mathrm{s}$
0.0 $\mathrm{m} / \mathrm{s}$
b) 2.20 $\mathrm{m} / \mathrm{s}$
1.39 $\mathrm{m} / \mathrm{s}$

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Physics 101 Mechanics

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Video Transcript

So here we have a diameter equaling 40 meters s O that automatically. We can say that the radius is going to be 20 meters and then she completes a lap in Delta T equaling 62.5 seconds. So just over a minute. And for party, they want the average speed for one for that lack. So she makes one circumference in that delta T one length of the circle. Essentially. So this would be to pi Times are or 20 divided by 62.5 and we're getting a 2.1 meters per second. This is her average speed again. She makes one complete revolution or one circumference length in that time interval. So to pi, times are two pi times 25 by 62.5. We're getting 2.1 meters per second. So this would be your answer for Part II on then. For part B, um, your average speed for half of this If we had, she completes half of the lap and 28.7 seconds. So here she has a circumference length divided by two on ly half a lamp on Lee, only half a lap. Other my apologies on then here, divided by 28.7 seconds. Now not 62.5. This will be 20 pie divided by 28.7, and we're getting an average speed of 2.20 meters per second for the first half of the lap. Now the velocity average. However, this is simply displacement. So if she's running in 1/2 circle and the circumference, um, is going to be and rather if the total distance travel is half a circumference length, that is the total distance traveled not to displace Schmidt. So for average, this average velocity we need to use the displacement. So be displacement over Delta T and the displacement. When you're when you're running 1/2 semi circle, the displacement is simply did diameter, so it would be the diameter divided by Delta T, and it would be 40 meters divided by 28.7, and this is equal in 1.39 meters per second. And again it makes sense because they make sense that the average velocity is less than the total displayed than the average speed. Because the total distance traveled is greater than the displacement. The diameter is going to be, of course, less than half a semi circle, half a circumference length. And that is the end of the solution. Thank you for watching.

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