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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Generally, no. Speed is actually a derivative function of position in mathematics, so its not possible to have a conversation about speed without talking about the distance covered in some amount of time.
Size of the object doesn’t really matter, because two objects traveling the same speed cover the same distance, regardless of size. Think of it like a train. A train with just the engine going 10mph will travel 10 miles in an hour. A train with 100 cars will cover the same 10 miles at 10mph – the caboose will be further back, but since it started further back it traveled the same amount of distance.
Speed is relative and only makes sense when you define a point of reference. A large object and a small object will cover the same distance if they are traveling at the same speed relative to the same point of reference.
But a larger object wouldn’t cover more distance, they’re traveling at the same speed. Typically, you’d have a reference point that you measure. So you’d look at a specific point on the large object and use that to determine the speed.
But no, distance is an inherent part of speed.
To answer the title of your question. No
Speed is literally a measurement of the rate of change in *distance* speed without any discussion of distance is nonsensical.
To answer your second question about the size. That also doesn’t matter. When we talk about speed we are basically say a specific *point* has traveled a given distance in a given time. The size of the object that point is attached to is irrelevant. Like this about it this way if you have a semi truck and a small compact car that both drive 60 miles in on hour. Did the licence plate on the semi travel faster than the license plate on the car? Of course not.
As others have said, no, there is not a way to measure speed that does not involve distance.
Speed is basically defined as distance over time. So without a distance you cannot measure the time or calculate the speed.
Speed and velocity are relative. What this means is that one object can only be assigned a velocity relative to a reference frame.
Basically, a car may only be moving 20 mph relative to the Earth’s surface, but 40 mph relative to an oncoming car, or 67,020 mph relative to the sun etc.
Large objects do not move faster than small objects. If we take something like the earth, we might use the center of it as it’s reference for distance in respect to other objects in space.
However, if you throw a ball, we will typically use the Earth’s surface as a reference point for speed.
When people say things like, “velocity is relative” they mean it entirely literally. There is no such thing as the velocity of an object without something else to relate it to.
TLDR; No. Speed and velocity are relative and by definition equal to Delta D / Delta T. Size doesn’t matter for this.
Nah. You define speed by the distance it moves over time, there’s no way of having speed without distance.
But that’s not a problem. There’s a bunch of other measures that are ratios. Frequency is literally “oscillations per second”, Joules are kilogram meters^2 /seconds^2. There are some fundamental measures, like length, mass and time, like you said, but almost all of the actual measurements we make are combinations of those fundamental measures.
As for “size” causing issues, there is no reason you cannot use the center of mass of the object for the speed in most cases. If the center of mass for your big object has the same speed as the center of mass for a small object, they’ll move the same distance.
If you can’t do that, you can integrate the different speeds of all the different parts and end up with a net speed anyway, so there’s never broken math.
>I realized that, unlike other measures that have their own units (length, mass, etc.), speed is measured using a ratio of distance and time
Speed is not special in this. Most physical quantities that we measure are defined by being ratios of other units. For example power is measured in Watts, but the definition of a “Watt” is kilograms * meters^2 / seconds^3 . We just give a special name to it because it’s easier to say.
You might find that ratio measurements are more common than you’d think. Take weight, for example: it’s a measure of force, which means it’s not just a “how much stuff” measure, but a “how much stuff being pulled so far per unit time squared.”
It’s about reference. Say you have a big wheel and a small wheel. If both wheels are travelling 100kmph, they’re going the same speed. However, the small wheel will be rotating much faster. So, if your frame of reference is rotations per minute, then the speed of the small wheel is much greater.
Same for your human racing a small dog point. That little dogs legs are moving much faster than the humans. So, you could say that the dog is moving its body faster than the human even though they’re both going 15kmph.
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