This question stemmed from a conversation about measuring the speed of two very different objects. I realized that, unlike other measures that have their own units (length, mass, etc.), speed is measured using a ratio of distance and time. So I was wondering, does the size of the objects get factored into the measurement somehow? If speed is only ever measured using this distance/time approach (mph, for example), then wouldn’t the measure of speed become problematic since a large object is able to cover more distance than a small object?
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The vast majority of units are ratios between other units, and you can reduce them down to a handful of “fundamental” units. Mass, distance, and time are some of the most common ones.
speed = distance/time
acceleration = speed/time
force = mass * acceleration
Or, in other words:
force = (mass * distance) / (time * time)
Some units, like force, get their own name because it starts to become unwieldy to call something a “kilogram-meter per second squared”, but when you’re doing physics, part of what you’re doing is breaking down what units are made up of what other units and seeing which ones cancel out or which ones combine to form a different unit.
For example, if I have *20kg-m/(s^2)* and I divide it by *10kg* then I have *2m/s^2*. A physicist or engineer would immediately recognize that you divided force by mass and got acceleration as the result.
You could make up a new unit for speed to give it its own name. In fact, there are several- *knots* are *nautical miles per hour. c* is the speed of light, or about *300,000,000 meters per second.* But, for the most part, distance divided by time is such an intuitive way to think about speed that people seem comfortable sticking with miles per hour or km per hour.
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