A GPS device tracks the elevation

Question

A GPS device tracks the elevation $E$ (in feet) of a hiker walking in the mountains. The elevation  $t$  hours after beginning the hike is given in the figure.

Notice that the curve in the figure is horizontal for an interval of time near  $t=5.5$  hr. Give a plausible explanation for the horizontal line segment.

Accepted Answer

Hi, everyone. Let's take a look at this practice problem dealing with the slope of a line. This problem says a car travels along a straight road and its distance D and miles from the starting point is recorded every hour. The distance traveled two hours after the journey began is recorded. Provide a reasonable explanation for the horizontal line segment located at about T is equal to five hours. Below the question. We're given a graph that has our distance D along the Y axis and our time T along the X axis, there is a curve drawn on this graph and there are points at one hour intervals located on this curve. We're also given four possible choices as our answers. For choice. A, the car might have accelerated during this time interval or choice B, the car might have stopped during this time interval or choice C, the car might have decelerated during this time interval. And choice D, the car might have immediately changed lanes. So we're going to be looking at for this problem, the horizontal light segment about the um time T is equal to five hours. Now, since we have a horizontal line segment. That means that our slope M is going to be equal to zero. To recall that your slope is equal to your change in Y divided by your change in X. And for a horizontal line segment, your change in Y is zero. And so therefore your slope is zero. Now, in the context of this graph, what does that mean? Well, the slope here tells us how our distance is changing at time at this given moment. And since our slope is zero, that means that there's no change in our distance. And the only way that that could happen would be if the car has stopped at least momentarily before it is taken off again. So if the car is stopped, there's gonna be no change in our distance. And so therefore, this is a reasonable explanation for this horizontal line segment. So that is actually the explanation that we're looking for. And if I look at our answer choices, the correct answer actually turns out to be choice B that the car might have stopped during this time interval. So I hope that this explanation has been useful and I'll see you in the next video.

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