The classic distance formula of rate×time=distance (or r×t=d) may not look like much. I wasn’t particularly impressed with it in elementary school when the teacher started discussing it. I wanted to learn new math that day, and this was just multiplication (or division if rearranged). Was it a new profound concept? No, just boring, mundane stuff. If you travel at this rate of speed for this amount of time,you end up traveling this distance. Being good in math and a fan of science fiction and science, I was hoping for something more interesting. But there’s more to this simple distance formula than meets the eye.
I can’t say I haven’t found the distance formula useful. In its original form, I’ve used it for finding a reasonable commute distance, based on average speed and desired driving time. I’ve also used it to find how far we will have traveled towards our vacation destination if we drive at a particular average speed for a given amount of time. Of course, it can be rearranged to provide the speed or time if given the other two. For example, if we try to travel a given distance in a given amount of time, would we end up speeding (much)? Or how long will it take us to travel a given distance at a given speed (will we get there before dark)?
But there’s even more to the distance formula from a STEM point of view. For starters, the definition of a light year is a direct application of the formula, since the distance that light can travel in one year (at the speed of light of course) is in fact one light year. Digging more into physics, the formula can be used to relate any wave’s speed, period, and wavelength, even for a radio wave traveling at the speed of light. The wave’s period is how long it takes to travel one wavelength. As another example, the distance traveled in just one part of a path can be expressed as the speed multiplied by the change in time, giving the change in distance. Change calculations like this are common in science and math and are related to calculus.
As already mentioned, the distance formula can be rearranged to calculate speed or time. It’s common in physics to calculate the average rate of speed by dividing the total distance by the total time. The speed can also be calculated for a part of the path, just like for distance. Simply divide the distance of that part by the the corresponding travel time. The speed can even be calculated for an arbitrarily small part of the path, if the distance and time for that smaller part are available. Getting the rate of speed for a very small part of a path is a fundamental concept of calculus.
This small handful of examples barely scratches the surface. As boring as I thought the distance formula was, it really has a lot of uses in science and math as well as in the real world. I just needed to be more patient and openminded and less arrogant. People who seem smart don’t always know best. At least now I can benefit from the distance formula, since I know more about it.
(c) Copyright 2021 by Mike Ferrell
Odd STEM 