paulo84 said:
OK, so time is change of displacement. Speed is change of change of displacement.
It has already been discussed, but IMO bears repeating. Time is NOT change of displacement. If s represents the displacement of some object, then a change in displacement is usually represented as ##\Delta s##. Velocity is the instantaneous rate of change of displacement, and can be written either as s' or s'(t) or ##\frac {ds}{dt}##. This last notation is the derivative of s with respect to t. "Change of change of <whatever>" is not good terminology. We always talk about the "rate of change" of some variable with respect to some other variable. In this context, the "other variable" is time.
Without getting too deep into the weeds of calculus (which is what we're really talking about when we are discussing derivatives), ##\frac {ds}{dt}## is defined in terms of a limit. IOW, ##\frac{ds}{dt} = \lim_{\Delta t \to 0}\frac{\Delta s}{\Delta t} = \lim_{h \to 0}\frac{s(t_0 + h) - s(t_0)}{h}##. Suffice it to say, that we can approximate the velocity by taking smaller and smaller time increments in doing the calculation.
Speed and velocity are different. Velocity is usually taken as a vector quantity, as it indicates a rate of motion in some direction. Speed, on the other hand, is a scalar quantity, with speed = |velocity|. A car's speedometer records the magnitude of the car's velocity, but doesn't indicate the direction.
paulo84 said:
Acceleration is change of change of change of displacement (or of distance, sorry I'm not sure whether acceleration is a vector or a scalar).
No, accleleration the rate of change of the velocity with respect to time. Again, if s is displacement, then s'(t) is velocity, and s''(t) or ##\frac {d^2s}{dt^2}##, also a vector quantity, as direction is significant.
paulo84 said:
It seems to me, with each new layer of change you're adding a new dimension.
No. Dimension has nothing to do with any of this.
paulo84 said:
Therefore there must be an infinite number of dimensions of space. Or am I getting space mixed up with motion?
Yes.