5 – 06 L Reasoning About Two Peaks H1 V1

You just made a plot of acceleration versus time for an elevator as it goes upwards from the ground floor and then stops two floors above. And that data looks something like this. Now, I want to call your attention to five regions of this data. The first section is from when I started collecting data into when the elevator just started moving upwards. The next section is that period of time when the acceleration is positive. This is where the elevator gets up to speed but it’s also when you might feel a little lurch in your stomach. Then the acceleration is pretty much zero for a while. This is when the elevator was just moving upwards at a more or less constant speed. Next, in this segment, the acceleration becomes negative for a few seconds and this is the elevator actually slowing down. Finally, this last region is just everything I collected after the elevator had stopped but before I stopped the accelerometer. And these two bumps, one in Region 2 and the other in Region 4, they looked very, very similar. The only obvious difference is that one is positive and one is negative. Besides that, they look basically like mirror images. And in fact, if you were to calculate the area under this curve and compare it to the area under this curve, you would find that they were exactly the same, except for the fact that A4 is negative in a sense, and that’s just because it extends down below the horizontal line corresponding to zero acceleration. This is not a coincidence. In the next few segments, I want to convince you that the area under the green curve corresponds to the total speed increase that happened in that time interval. And the area under the red curve corresponds to the total speed decrease that happened in that time interval. For now, I want you to think about this elevator’s motion a bit more.

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