Einstein's general theory of relativity question

Question

I have a question about Einstein's General Theory of Relativity. I know little to nothing about quantum physics given I'm only in 7'th grade. But I was watching a lecture on this theory, and I had a question. The formula for acceleration is the time derivatives made up of the three main coordinates (x, y, and z,) but as I was saying acceleration's formula is made up of the second derivatives of the coordinates divided by another second derivative with respect to time by you get acceleration. And if you just have a derivative of the coordinates divided by another derivative with respect to time you get velocity to my understanding. And so if you multiply velocity by two or it's components by two will you get acceleration? As I said previously I know almost nothing about quantum physics because I'm in 7'th grade so this is sort of a dummy question, and I hope it made sense so I can get an answer.

Answer 1

There are quite a few things to unpack here. 1) Quantum Physics has to do with light and particle interaction at the subatomic level. 2) Relativity has to do with things going near the speed of light and how that effects time (special) and how gravitation is a warping of space (general)

Neither of these modern theories has to do with your question which is about acceleration, velocity, and position (Newtonian Mechanics)

velocity is the rate of change of position: change of position/ change in time, or Δr/Δt and in the limit as Δt approaches 0 (a moment in time) dr/dt.

The relationship between acceleration and velocity is similar because acceleration is the rate of change of velocity with time or Δv/Δt or dv/dt.

What you are asking about has to do with calculus, partially invented by Newton to deal with acceleration and forces that change with time.

The acceleration is dv/dt = d/dt (dx/dt) = d²x/dt² for one space dimension. The two is not a multiplier nor a simple squaring, but a symbol that a change operator was used twice. The acceleration is the rate of change of the rate of change of position.