Scaling Bezier curve first and second derivative?

Question

I'm trying to use a cubic Bezier curve for ease-in-ease-out movement in 1 dimension. The output is position, first derivative is velocity, and second derivative is acceleration to control a motor. But a Bezier curve is defined in terms of 0-1 and I might need to move 1.9 meters. For position, I can multiply (e.g. by 1.9) to scale, but is there a way to scale the first and second derivatives?