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In quantities such as speed where the derived (SI) unit is m/s, why do we pronounce it and interpret it as meters per second? My guess is that 1 m is associated with 1 second. Similarly, 5 m/s is pronounced and interpreted as 5 meters per second, because 5 meters are associated with 1 second. I am not sure whether this view is naive.

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closed as off-topic by Michael Seifert, stafusa, M. Enns, Chris, Cosmas Zachos Feb 18 '18 at 17:19

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    $\begingroup$ 5 meters per second means 5 meters for each second, i.e. every second an object with that speed moves by 5 meters. What is not clear about that? Similarly, 50% (50 per 100) is 50/100, that is 0.5 $\endgroup$ – Stéphane Rollandin Feb 17 '18 at 17:23
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    $\begingroup$ I'm voting to close this question as off-topic because this seems to be more about English language use than about physics. $\endgroup$ – Michael Seifert Feb 17 '18 at 17:32
  • $\begingroup$ @StéphaneRollandin That makes sense. It is the case that we can always translate a/b to 'a' per 'b' and vice versa in Mathematics and Physics? $\endgroup$ – Supernova Feb 17 '18 at 17:37
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    $\begingroup$ I wouldn't say always. For instance, it would be unnatural to read "1/2" as "1 per 2." In my mind, reading "a/b" as "a per b" would be unnatural unless it is known to be a rate of some sort. $\endgroup$ – Chris Feb 18 '18 at 7:02
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It is an instantaneous value. The speed, in m/s (or any other unit) is:

$$\frac{ds}{dt} $$

where $s$ is distance/displacement. If speed is constant, it really doesn't matter: an object moving at 5 m/s will cover 5 m in every second.

It will be very different if the speed varies. Imagine a dropping stone, subject to a 10m/s/s acceleration. At 1 s, the instantaneous speed is 10 m/s, but that speed occurs for exactly zero time.

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