Why is speed/position relative but acceleration not? [duplicate]

This question already has an answer here:

I think i understand it now, if found this: link

I know that position and speed are relative. There is no such thing as universal coordinates. Then why is acceleration absolute? Is the 3th and 4th derivative of position to time also absolute? Where/how can i see this in the math/laws of motion?

For example: you are in a rocket and you have an accelerometer with you, and someone else is standing on an astroid that is not attracted by gravity towards something else, so it has no net force on it. If the engines of the rocket are turned on, then you will see that on the accelerometer, and you will know that it is you that is accelerating, not the astroid.

Also if the universe were completely empty, except for a bucket of water. If the water would be pushed towards the edges of the bucket, then we would know that the bucket is rotating around its axis. But what would happen if you could rotate space itself around the bucket?

It probably is because $F=ma$ and not something else like $F=m^2a^3+2a+...$, is that correct? Can $F=ma$ be deduces from deeper principles, or is it an experimental law?