My idea doesn't require any new types of rails. I want to be able to control the speed of a minecart without the need for Railcraft, as its system of speed control has issues (I'll get to that).
It would be this: if a powered rail has a full 15 power from the adjacent redstone, it makes the minecart travel at a speed of 15 (obviously not blocks per second, that would be fast - speed 15 would equate to what's already the normal minecart speed, or even faster1) and transmits the power to the rails up to 8 blocks away from it, just like it already does.
However, if the rail is given 14 power from the adjacent redstone, it only gives a speed of 14 and transmits to the rails up to 7 blocks away.
For x power given to the rail, the minecart has speed x, and the adjacent x/2 rails (assuming they're powered) are powered as well with the same speed as the rail originally powered (otherwise it would be ineffective to connect powered rails and nobody would do it). If the power value is odd, round up for the number of additional rails in each direction powered, unless the power is 1. In that case, only the single rail would be powered. If the power is 0, then, just like it is now, the rail effectively stops the rail.
Note: I understand that when you hit a powered rail, you don't instantly go to top speed or instantly stop. I'm saying that those rails would have a set speed of the power value, so that they would bring the minecart towards that speed (whether that means acceleration or deceleration).