What does meters per second per second mean?

Question

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

Answer 1

The fundamental subject is dimensional analysis, and you kind of have to understand derivatives and integrals to fully get it. But the ELI5 key is to understand some measurements are dimensions and others are derivatives, which means they are derived from the dimensions. The most common dimensions are space and time. ‘x, y, and z’ Cartesian coordinates are spacial and refer analogously to oneself as forward/back, left/right, and up/down. Time generally moves in one direction, forward.

So, the base measurement is time, ever second a second passes. Simple enough.

The first derivative/derived measurement, is velocity. If one second passes and you move 1 meter in a particular direction, then another second passes, and you move another meter in the same direction. You are moving 1 meter every second, 1m/s,

The second derivative/derived measurement, is acceleration. If one second passes and you move 1 meter in a particular direction, then another second passes, and you move another 2 meters in the same direction, then a third where you move 3 additional meters, etc. You are not moving at a constant velocity, but are accelerating at a constant rate. Every second that passes, your velocity is increasing by 1 meter per second, thus one meter per second, . . . per second.

Absent relativistic effects, time is constant, but at any moment in time your position, your rate of movement [velocity], and your rate of acceleration can change, That goes back to the key mentioned above, derived measurements are measurements of change relative to constants like space and time. Under the concepts of time, position, speed and acceleration, their relative relationship is always the same, because they are defined relative to each other. And the expression of the changing values is expressed in terms of that relationship. No matter the measurement system, position will be a coordinate [ie, x,y,z], velocity will be a change in position over a period of time [change in distance over change in time dx/dt], and acceleration will be a change in velocity over a period of time [change in distance over change in time over change in time d^2x/dt^2].