Graph 3. Xander and Zach are racing each other from Frisco...

Graph 3. Xander and Zach are racing each other from Frisco to Denton, a distance of 20 miles. Xander covers 10 miles in 10 minutes, before being stopped at a red light for 3 minutes. Then he finishes the final 10 miles in ten minutes. Zach drives at a steady rate, never having to stop for a red light, and covers the 20 miles in 23 minutes. Velocity (miles / minute) Find the area under the curve for each boy. This can be done with some geometry. Don't forget units! What is significant about the area under the curve for each boy? 0 time (minutes)

Transcript

00:01 So in this problem we're going to be plotting velocity and time.

00:03 So the first thing we need to do is find that velocity.

00:06 Now velocity is defined as distance over time.

00:12 So for xander, the velocity, he covers 10 miles in 10 minutes, and so that gives us 10 over 10 is 1 mile per minute or 60 miles an hour, so highway speeds.

00:29 Now that's the same for both blocks of his motion because he moves, stops, and then moves again.

00:36 So then we can also look at the velocity of zach, 20 miles in 23 minutes, and i'm going to leave this in the fraction just because we don't need to convert and we'll see it cancels out later.

00:49 So now we can plot this.

00:52 So we have our axis, our time in minutes, and our velocity in miles per minute.

01:03 So xander travels a distance over time and then stops.

01:06 Now this is for the first 10 minutes and moving 10 miles in that 10 minutes on average, we figured out that velocity was 1 mile per minute.

01:16 So assuming constant velocity, he instantly magically comes up to speed at a constant velocity and then instantly stops, and this value here is 1 mile per minute is the unit of course on this axis.

01:30 Now xander is stopped for 3 minutes, so 10 plus 3 is 13 minutes, and then once again starts, travels, and stops for 10 minutes, so 13 plus 10, 23 minutes.

01:45 Now xander travels a constant velocity of 20 miles in 23 minutes.

01:49 So what is his velocity, 20 over 23? now we can see that's somewhat less than 1.

01:57 So this is the xanders in black here, and then we can say zach in green, and then the velocity here is 20 over 23.

02:17 So now we can find the area under each of these curves.

02:19 So for xander, we have two areas to consider, and then for zach, we just have the one.

02:29 Now these are rectangles, so the area is going to be equal to the base times the height...

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