You can explicitly work out a length function, e.g. as a function of your interpolation parameter, using integration, but this is complex and still gives you something difficult to use. If you are doing your updates often enough you can make this easier by breaking down the motion along the curve into enough short linear steps.

E.g. At time 0 you are at x and want to get to x'' at time t. If the time t is short enough and the curve is smooth then the path from x to x'' will be close to a straight line, and the distance along the curve can be approximated by the straight line from x to x''.

First guess the parameter needed (e.g. by assuming it increases the same as last time) and work out the coordinates of x''. Work out the distance d from x to x''. Compare this to the desired distance = speed * t, and use the ratio of it to d to rescale the parameter increment, e.g.

increment = guessed increment * ((speed * t) / d)

For a smooth curve and small enough steps this should produce reasonable results. To improve it''s accuracy use smaller time steps and/or recheck the distance and repeat if necessary, e.g. if the distance is still out redo the cacluations using the newly caculated increment as a starting point.