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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A large object traveling at 20 mph goes at the same exact speed as a small object traveling at 20 mph. The larger object will only cover a greater distance in the same amount of time if it increases its speed.
Your question is kind of like asking if there is a measure of volume that does not depend on space. But volume only makes sense as a concept if we refer to space. Because volume literally depends on how much space something takes up. That’s what volume fundamentally is.
For rotational motion, there’s angular velocity, which is sometimes used. For instance RPM (revolutions per minute) in a car engine is independent of the size of the engine, piston size etc. just depends on how many times the crankshaft turns per minute.
Additionally you could say a second hand rotates at 1 RPM, a minute hand 1/60th of an RPM etc. regardless of the length of that second hand, it’s the same for a wristwatch as for Big Ben.
While this is excellent for rotating objects, this isn’t a good way of measuring velocity when you’re wanting to actually know linear velocity.
Funnily enough, it’s actually the opposite way round, now. Speeds are effectively measured compared to the speed of light, because distance is really defined based on how far light can travel within a specific time.
But, that’s a bit of a long story. The other part of your question is about the size of something, and if that affects speed. Say there’s a train that’s a mile long, and the back of it is right at the start of the track. The front of the train is at the 1mile marker. Suppose after an hour, the front of the train is now at the 2 mile marker. Would you say the train has travelled at a speed of 2mph? No, because the train hasn’t *travelled* 2 miles, only 1 mile. The length doesn’t matter. It just matters how far each bit of the train has moved, and each bit has moved 1 mile.
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.
Lots of measures are a ratio. Density, for instance, is measured in mass over volume, e.g. grams per liter, or kg per m^(3). Current is measured in amperes, but an ampere is defined in terms of the number of elementary electric charges that move through a conductor every second (1 ampere equals 10^(19) coulombs per second, where a coulomb is the standard unit of charge). So current is measured as charge per second. The list goes on. Speed is by no means the only measure that is like this.
A large object is not able to cover more distance than a small object, I don’t know why you think that. Its footprint may be larger and so in that sense it covers a larger area, but you can move a large or a small object by the exact same distance, and how quickly you do that determines the speed.
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