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I have been pondering over a concept regarding the general formula for acceleration, which is widely accepted as $\frac{m}{s^2}$. This formula elegantly illustrates that a given mass or body is accelerating at a rate of m meters per second every second.

However, my contemplation led me to consider an alternative formulation, namely $\frac{m}{sM}$, where $m$ represents meters, $s$ represents seconds, and $M$ denotes minutes. In essence, this formulation suggests that a body or mass accelerates at a speed of m meters per minute for every passing second.

I am curious to explore the validity of this proposition and would greatly appreciate your insights on the matter. Specifically, I would like to address the following inquiries:

  1. Is the proposed formulation incorrect?
  2. If it holds merit, what impediments prevent its widespread adoption or inclusion in academic discourse?
  3. Alternatively, if it is flawed, could you kindly elucidate on the specific deficiencies in the concept?

Thank you for considering my doubts and for your time and attention to this matter.

PS: I am currently in 9th grade and encountered this doubt while studying accelerating bodies.

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    $\begingroup$ Those units are valid, but what advantage would they have? $\endgroup$
    – Ghoster
    Commented May 8 at 17:11
  • $\begingroup$ @Ghoster if they are valid, why always use $\frac{m}{s^2}$? Why don't we see it anywhere. And, about the part of the advantage, isn't that the same as why use kmph when we have m/s ?? Please do correct me if I'm wrong $\endgroup$
    – Sambhav Khandelwal
    Commented May 8 at 17:13
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    $\begingroup$ Meters per second per second is the standard unit for acceleration in the Système international d'unités (SI). You don’t have to use it if another unit is more convenient. We do not “always” use it. $\endgroup$
    – Ghoster
    Commented May 8 at 17:17
  • $\begingroup$ It again depends on widespread use, The unit is perfectly valid , But Standard unit "seconds" is widely used, Hence more popular $\endgroup$
    – Dheeraj Gujrathi
    Commented May 8 at 17:17
  • $\begingroup$ Thanks everyone here for letting me know that this unit is right :). $\endgroup$
    – Sambhav Khandelwal
    Commented May 8 at 17:19

2 Answers 2

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There is nothing inherently wrong with this, it's fine to replace any unit of measurement with any other equivalent unit of measurement. 1 minute is the same thing as 60 seconds, or 1/60th of an hour - there is literally no difference between them. The behavior of a physical system obviously should not be determined by the units you choose to describe it.

The earth's gravitational acceleration is 9.8 meters per second per second, or 980 centimeters per second per second, or 588 meters per second per minute - expressed in words, this means that a freefalling object will accelerate by 588 meters per second over the course of 1 minute.

The issue is that there's often no particular advantage to using such a unit - it doesn't produce any different result, and will sometimes just require the use of conversion factors between different units of time which would not be otherwise required. Seconds are SI units and are very widespread. Expressing an acceleration as meters per second per minute isn't wrong, but it would be quite unusual.

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I have seen kilometers per hour per second and miles per hour per second. I haven't come across meters per minute per second before but there's nothing wrong with it. It's just that meters per minute is not commonly used as a unit for speed so there's not much use for meters per minute per second.

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    $\begingroup$ Miles per hour per second would be useful if you have a car that can go from 0 to 60 mph in 5 seconds. $\endgroup$
    – mmesser314
    Commented May 8 at 18:08

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