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
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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