what is the significance of seconds squared [s^2]?

59 views
0

Time moves at one constant. How can you have it raised to an exponent? If you have say: 3 seconds^2, is it actually 9 seconds?

In: 5

It’s significant in things like acceleration. But thinking of it as “seconds squared” kind of obfuscates what is really going on. Acceleration isn’t as much a “distance per seconds squared” as it is “velocity per seconds” and velocity itself is “distance per seconds.”

For example, your acceleration might be 9.8 feet/second^(2). What that means is, for every second that passes, your velocity increases by 9.8 feet/second.

>If you have say: 3 seconds². is it actually 9 seconds?

No if you square units you have that unit twice. 3m² are an area and not 9m length.

Squared seconds rarely matter alone. But having something per squared second often makes sense. For example m/s² is meter per second per second (so speed per second, wich is how much you accelerate)

You can have more abstract variables that are of the unit s², not something “directly measurable” though. For example “length per acceleration” would be in s², and that might come up if you measure acceleration with a spring-mass system (the variable would then describe the measure sensitivity)

There is a better way to think about it. Take acceleration, for example. It’s units are distance/time^2. But this can also be written as (distance/time)/time. So, it’s really more about the rate of change of speed. How is the speed changing second to second. Mathematically, it reduces to seconds squared, but logically, it’s more about the rate of change of something like speed

When you have s^2 as a unit, usually in a physics quantity, you do not square the number to get seconds. If a term is acceleration (m/s^2 ) then if you multiply by 5 seconds it cancels out one of the seconds in the denominator and gives you m/s = velocity.

These techniques, what’s sometimes called units analysis, allow you to have numbers with more meaning. Having a weight of 5g is more meaningful that just having a weight of 5.

It means you are taking multiple rates.

My position is measured in meters.

My position is changing! My velocity is measured in how much my position changes with time. My velocity is measured in meters per second.

But my velocity is also changing! My acceleration is measured with how much my velocity changes with time. My velocity is measured in meters per second per second. or meters per seconds^2 .

… and so on.