Timeline for Why is acceleration expressed as m/s/s?
Current License: CC BY-SA 3.0
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| Jan 31, 2014 at 6:58 | comment | added | Luboš Motl | Maybe you are asking why "per" is represented by the "slash", "/". It's because this sign means mathematically "over", the word indicating dividing (division) and division is the opposite of multiplication. For example, if someone accelerates at the acceleration 10 m/s/s for 7 seconds, then he changes his speed by 10 m/s/s times 7 s = 70 m/s (that was multiplication). Note that one of the "s" canceled because s/s=1. This relationship may be reverted. If the speed change is 70 m/s and it takes 7 seconds to achieve it, the (average/constant) acceleration is 70 m/s / (7 s) = 10 m/s/s. | |
| Jan 31, 2014 at 6:39 | comment | added | Luboš Motl | Dear @Hal, $(m/s)/s=m/s^2$ is the unit of the rate of increase "per second" because the final denominator is "/s" i.e. "per second". The numerator is "m/s" which tells you the unit of what is the something that is changing per second. It's the speed, so its unit is m/s. Acceleration is the change of speed per second, so we add another /s at the end. It is completely analogous to the question why the unit of speed is m/s. It's the rate of changing the location or distance in meters which we get each second, therefore m/s i.e. meter per second. I can't possibly understand what may be confusing. | |
| Jan 30, 2014 at 22:58 | comment | added | Benjam |
Replace increasing with changing and speed with velocity and you'll have the proper definition. Acceleration is the rate by which the velocity is changing at a given moment. When you throw a ball in the air, it's acceleration is 9.8 (m/s)/s in the downward direction. Since it's initial velocity was in the upward direction, the speed is decreasing but at a constant rate of 9.8 (m/s)/s. Once it's at the top of it's arc, the acceleration is still the same, and therefore it starts falling. The acceleration was constant through the whole flight, only it's velocity changed.
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| Jan 30, 2014 at 22:50 | comment | added | Hal | @LubošMotl thank you. That actually helps quite a bit. But, one core part of my question remains: acceleration is the rate by which the speed is increasing at a given moment. How does the expression (m/s)/s convey anything about an increase in anything? | |
| S Jan 30, 2014 at 20:35 | history | suggested | Peter Mortensen | CC BY-SA 3.0 |
Copy edited. (its = possessive, it's = "it is" or "it has". See for example <http://www.wikihow.com/Use-its-and-it's>.)
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| Jan 30, 2014 at 20:33 | review | Suggested edits | |||
| S Jan 30, 2014 at 20:35 | |||||
| Jan 30, 2014 at 19:24 | comment | added | Kyle Oman | @Hal I think a better english statement would be "the number of (meters per second) that an object accumulates in a second". The parentheses you used in your question are very helpful in guiding intuition. | |
| Jan 30, 2014 at 17:36 | comment | added | Luboš Motl | Acceleration is not an accumulation of speed (much like the upward speed is not accumulation of the elevation). An accumulation of speed over an interval (i.e. the integral of acceleration) is the speed difference between the final and initial moment and it has units of velocity, m/s, not the units of acceleration. Acceleration is not accumulation; acceleration is the rate by which the speed is increasing at a given moment. The whole point of the acceleration is that it is the derivative of the velocity, and the derivative is sort of the opposite thing than accumulation (integral)! | |
| Jan 30, 2014 at 17:06 | comment | added | Hal | Thank you. The problem I saw with my understanding: I presume, that (m/s)/s or m/s^2 are complete definitions of acceleration. However, I do not see anything in those expressions that defines acceleration as the accumulation of speed. I.e. in English we might express (m/s)/s as the number of meters a person travels in a (or in x) second(s), in a (or in x) second(s). To me it seems like the notion would be better expressed (and I don't know better, which is why I presume I'm misunderstanding) as the difference between the speed of a thing at one instant and its speed at another instant. | |
| Jan 30, 2014 at 14:45 | history | answered | BMS | CC BY-SA 3.0 |