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
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
>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)
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.
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.
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.
Acceleration is measured in meters per second per second (not a typo). It looks better to write 5 m/s^2 than 5 m/s/s which is exactly the same thing.
Trying my best to ELI5 here.
If you sit on a train stuck at rest at the train station, your speed is 0 m/s. Every second that elapses, you move 0 meters. The amount of distance you cover (change in position) over an amount of time is your average speed (meters per second, or m/s) over that time. Your acceleration, or change in speed over time (m/s/s), is also 0. Since your taking a rate (m/s) and finding the rate of change of that rate(m/s/s), the denominator of that quantity is now s².
Now let’s say you were on a train cruising along at 30 m/s. Every second that elapses, you move 30m. You move 30m/s now, you will move 30m/s in 5 seconds, and you will move 30m/s in 30 seconds. Therefore your speed is being maintained, so your acceleration is 0 m/s/s or 0 m/s².
In both instances above, a graph of position (y axis) vs time (x axis) is a straight line – when you’re at rest the line is the same as the x axis. When you’re moving 30m/s, the line is a straight line with a slope of 30m/s.
Now imagine your train leaves the station and you start a stopwatch at that moment. It takes you 30 seconds to get up to your 30 m/s cruising speed. Each second, your train picks up 1 m/s of speed. Your position over time will look like the right side of a parabola. (See left graph in link below). Now, the slope of that parabola at each individual point is the train’s speed. If you plot the slope of the position graph (spe onto its own graph, with time as the x axis still, you now have a straight line with a positive slope. This is the middle graph. Now if you take the slope of that straight line and plot it against time again, it’ll be a horizontal line. This means that regardless of if you look at the acceleration at time t=1 or t=10, the y value is still 1, and the unit is m/s/s or m/s².
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcS-_dpEEjml-ES-_XSpMcTFvJJW_wFhLtSiCQ&usqp=CAU
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