I googled this but I still don’t get it. I’m not mathematics inclined at all so literally make this a ELI5!
In: 11
You know when people talk about how fast a car can accelerate they say stuff like:
> “Zero-to-sixty (mph) in 4.72 seconds!” (in America)
> “Zero-to-one-hundred (km/h) in 4.88 seconds!” (in not-America)
This means that the car can go from a speed of 0.0 mph and get up to 60.0 mph in 4.72 seconds. On average, this means that the car increases speed by (60.0mph)/(4.72s)=12.7mph/s which makes sense: after 1s you’re up to 12.7mph, by 2s you’re up to 25.4mph, by 3s to 38.1mph, 4s to 50.8, and 5s to 63.5… which means we must have “hit 60mph” around that last quarter of a second (so it looks like our math did work out correctly).
But, mph is a derived unit of “miles per hour” which means that 1mph=1mi/h and so we could also write our math above out as 12.7mph/s=(12.7mi/h)/s… which, if we deal with all the numerators and denominators correctly, means that (12.7mph)/s=(12.7mi)/(h * s) or 12.7 miles per hour-second. Now, that might sound like a weird way to write things out, but in a lot of complicated mathy situations it is a nicer to have just one numerator and one denominator rather than having a bunch of nested fractions to keep track of.
Meters per second squared is the exact same kind of thing, except instead of measuring speed in mi/h it is measured in m/s. That means, because 12.7mph=5.68m/s that our (1.27mi/h)/s calculation is equivalent to (5.68m/s)/s and the car is accelerating by 5.68 meters-per-second every second – or if we do the simplified-fractions math – the car accelerates 5.68 meters per second-second. (Or, in other words “5.68 meters per second-squared.”)
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