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Is it merely an arbitrarily chosen definition that we created in order to quantitatively measure the speed of an object or is it some other way around. I want to know what's the reason behind such a relation?

NOTE : I’m considering the fundamental case wherein the motion is uniform and is along a straight line.

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    $\begingroup$ Are you talking about instantaneous speed or average speed? $\endgroup$ – Qmechanic Oct 24 '18 at 8:35
  • $\begingroup$ @Qmechanic I’m considering the simplest case wherein the motion is along a right line and is uniform $\endgroup$ – user596245 Oct 24 '18 at 9:04
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    $\begingroup$ Any quantity in physics is an "arbitrarily chosen" definition. How useful this definition is for measuring and understanding reality determines whether or not it sticks around. $\endgroup$ – Aaron Stevens Oct 24 '18 at 9:57
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    $\begingroup$ Possible duplicate of Why is speed defined like it is? $\endgroup$ – FGSUZ Oct 24 '18 at 10:36
  • $\begingroup$ I honestly don't understand the motivation for this question. If one measures the distance $d$ an object traveled with a ruler and measures the elapsed time $t$ with a clock, the ratio $d/t$ is a physically meaningful quantity whether we call it speed or something else. Are you asking why $d/t$ is physically meaningful? $\endgroup$ – Alfred Centauri Oct 24 '18 at 11:13
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Italian physicist Galileo Galilei is usually credited with being the first to measure speed by considering the distance covered and the time it takes. Galileo defined speed as the distance covered per unit of time.[3] In equation form, that is

$v=\frac{d}{t}$

where $v$ is speed, $d$ is distance, and $t$ is time. A cyclist who covers 30 metres in a time of 2 seconds, for example, has a speed of 15 metres per second. Objects in motion often have variations in speed (a car might travel along a street at 50 km/h, slow to 0 km/h, and then reach 30 km/h).

https://en.wikipedia.org/wiki/Speed#Historical_definition

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  • $\begingroup$ Wikipedia's story seems pretty far-fetched. Galileo wasn't around 'til the 1500's, but I pretty strongly suspect that people have understood the concept of distance-per-time since pre-history. $\endgroup$ – Nat Oct 24 '18 at 8:36
  • $\begingroup$ Yeah that must be the case. Then again, i think this is as good an answer anybody will ever got to this question. $\endgroup$ – DakkVader Oct 24 '18 at 9:10
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If you consider how such a quantity may have come about, you could believe that it would be most useful to the average person when making comparisons between every day occurrences involving movement.

My assumption is that the concept of speed would have arisen in an "every day" context rather than coming into being as a pure mathematical definition.

A related answer in Stack Exchange states that the concept of speed predated Galileo by a long way which supports this assumption.

For example, consider an historical era predating free access to basic education, pre-calculus, where a horse travels 10 leagues in a day, whilst another travels 6 leagues in half of a day. How might someone in some historical, compare which is fastest?

You need an averaged quantity that describes the rate at which the horse travels i.e. you would have to long it takes each horse to travel the same distance. To my (admittedly biased) mind, this leads naturally to the concept of speed but without the definition we now use without hesitation.

Obviously, we know that, in this example, one horse travels 10 L/day whereas the other travels 12 L/day, and we, without modern educations, interpret those quantities as speeds.

Therefore, I believe the concept of speed is simply a result of we humans wanting to make simple comparisons of moving objects in Nature, which has eventually been made rigorous in its meaning, and even been extended through calculus to the concept of instantaneous speed.

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Ask yourself how one goes about measuring speed: you always measure the distance and the time and divide the former by the latter. Notice that you don't need to consider the speed of an object to know how far it's traveled from some point, nor do you need the speed of the object to measure the time it takes for the object to travel from one point to another. It is in this sense that length and time are more fundamental than speed.

Because speed cannot be measured in a simpler, more fundamental way, it makes sense to define it as distance divided by time. Loosely speaking, quantities are defined by how we go about measuring them.

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