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Why did physicists develop the concept of velocity? I searched on the web, but I didn't get a satisfactory answer. All I got is that velocity has a direction whereas speed does not. Why do we need concept of velocity? If we could consider speed as a vector quantity, would it make any difference?

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  • $\begingroup$ velocity is the same as speed except that it has direction. If we consider speed as a vector quantity, it becomes velocity. that's all. $\endgroup$ Jun 12, 2023 at 4:49
  • $\begingroup$ This does not seem to be so important, as there is no such distinction in German, for example. $\endgroup$ Jun 12, 2023 at 4:57
  • $\begingroup$ This site is being inconsistent as here is a closed duplicate What was the need to introduce the term 'velocity '? but there is an answer on a sister SE site Why are 'speed' and 'velocity' not given the same name? $\endgroup$
    – Farcher
    Jun 12, 2023 at 7:40
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    $\begingroup$ Having done some investigating I am sure that this post should migrate to History of Science and Mathematics SE. As an example in a textbook written in 1871 it appears that velocity is the term to use if measured in feet per second and speed is to be used if the unit is different eg miles per hour!! Just read paragraph 4 onwards to be amazed? $\endgroup$
    – Farcher
    Jun 12, 2023 at 8:12
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    $\begingroup$ I want to point out an amusing coincidence that's also a nice memorization technique for anyone that's new to physics and is still getting used to this terminology: observe that velocity is a vector, while speed is a scalar ;-) $\endgroup$
    – Amit
    Jun 27, 2023 at 23:07

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It's really not an important distinction. Speed is really just the magnitude of the velocity. As HolgerFiedler said, in German there's not even a distinction made.

We certainly could just have velocity and say "the magnitude of the velocity" rather than "the speed" when needed, or have made speed a vector and say "the magnitude of the speed" rather than have the word "velocity". It's just a minor convenience to have two different words.

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Speed is a scalar, and velocity is a vector. They are geometrically different.

With $s =|\vec v|$, momentum:

$$ \vec p = m \vec v$$

is a manifestly rotational covariant equations, while:

$$ KE = \frac 1 2 m s^2 $$

is manifestly invariant.

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It seems you are not asking about the concept of velocity, which you seem to understand why it exists and why it is a vector, but just why in English this French-derived word was used over the older Old-English-derived word "speed".

I guess that, simply, people have been using the word "speed" for ages for the magnitude of the speed. People say "My car's speed is 50 Mph", not "My car's speed is 50 MPh going northeast". When they wanted to look at a vector speed - magnitude and direction - they just adopted a different, more formal-sounding (i.e., French) word. Having mulitple words for similar things - one of Germanic origin and a more "technical" one with French origin - is a common thing in Elgish.

It's worth noting that this is a word choice made in English, and doesn't carry to other languages. In Hebrew, for example, the word used for a car's speed, מהירות ("mehiroot") is also used for the vector velocity in Physics. When a Hebrew physicist wants to talk about the magnitude of the velocity, he or she uses "the magnitude of the speed". We don't have a separate word for it.

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Why had physicist developed the concept of velocity ?

We need to use a vector rate of change of position - rather than its scalar magnitude - in the definition of momentum so that momentum is conserved.

If we defined momentum as $m|\vec v|$ instead of $m\vec v$ then momentum would not be conserved in general. To see this, consider two equal masses approaching one another with velocities that are equal in magnitude but opposite in direction. $\Sigma m \vec v$ is zero both before and after they collide, but $\Sigma m|\vec v|$ is only conserved if the collision is perfectly elastic. A definition of momentum that was only conserved in certain specific circumstances would be a much less useful definition.

If we could consider speed as a vector quantity. does it make any difference ?

Whether we call the vector rate of change of position speed or velocity or something else is a matter of convention.

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Somewhere around 1880 "formal" definitions of speed and velocity were adopted by (English speaking) Physicists and those definitions are now in common usage.

After 140 years it matters not as to whether one should use but one word instead of two, like for a lot of things, common usage over time prevails; just think of conventional current, the right-hand rule etc.

And the differentiation does have some virtue?

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