Detailed minecart physics in Minecraft

Minecart physics can be found on the Minecraft Wiki page for Minecarts. I think what you are looking for is under Loss of Speed:

One unit of kinetic energy could be defined as the energy gained by a cart going down a one block slope, and lost by a cart when it goes up a one block slope.

If a 45 degree downward slope is connected directly into an upward slope, an initial height of 60 blocks will result in a final height of 40 blocks, a loss of 20 units of potential energy. But if 20 sections of flat track are inserted between the slopes, the final height will be 35.

This implies that one unit of energy is lost for every 4 sections of horizontal track traveled with an initial stored energy of between 60 and 40. At much lower speeds, much less energy is lost, implying that the energy lost is a percentage of the cart's current energy. The above gives about 0.5% energy loss per section of track.

One implication of this is that more energy lost when the cart has more energy, so a gradual slope should allow you to travel much farther distances than a steep slope followed by a long flat section. (This is different from real-life physics, where friction does not increase with velocity. However, it may be an attempt to mirror air resistance, which does increase with velocity.)