How to Use Your Speedometer to Figure Out The place Your Auto Is

Let’s imagine that you are in a motor vehicle with no home windows. I know that is insane, but just keep on. Even though there are no home windows, you can see the speedometer. So, here is the issue. Is it attainable figure out how significantly you have traveled just by seeking at the speedometer? This is a basic physics problem—and we are likely to do it in actual lifetime. It really is heading to be pleasurable.

I am going to get started with some idealized cases so that we can determine out how to get the job done this trouble. Then we can get to check out it on serious data—a video clip of my car’s speedometer. It will be a actual-existence physics problem.

Let’s start out with a easy scenario to make guaranteed we know what’s heading on. Suppose I have a automobile going at a regular pace of 10 meters/second for 5 seconds. Considering the fact that the motor vehicle is going with a frequent velocity (in one dimension), I can create the adhering to as the definition of velocity.

Illustration: Rhett Allain

In this expression, Δx is the change in placement (the displacement) and Δt is the sum of time (the time interval). If I algebraically solve this for Δx, I get:

Illustration: Rhett Allain

With a velocity of 10 m/s and a time of 5 seconds, that presents a displacement of 50 meters. See, that was easy. You almost certainly could have done that in your head. But hold out, you can find yet another way to glimpse at this difficulty. What if I make a graph of the velocity as a function of time? Of course, this would be a uninteresting graph—but let’s do it anyway. Here’s what it would seem like.

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