Hope you are able to catch all of that. I might just look at the minecart source code and come back to see how each bit affects the speed momentum etc.
I think I followed it. The more I look into minecarts and their odd behaviors, the more I believe that the tick-based nature of Minecraft makes things more complex than what you described. For instance, let's say you have a minecart that's at a maximum speed of 0.6 meters per tick (that's not the actual maximum, but let's just use that as an example). This minecart passes over a powered rail. Each tick the Minecraft engine increases the cart's momentum, and then moves (teleports) it 0.6 meters. If the first time the minecart was on the powered rail it was at 0.2 meters in, on the next tick it will be at 0.8 meters and it will get boosted a second time. But if the first time it was on the powered rail it was at 0.5 meters, it's only going to get boosted once.
This discrete updating, as opposed to the effectively smooth updating that we get in the real world, makes all our velocity/momentum models of minecart behavior break down if we look too closely.
I think I followed it. The more I look into minecarts and their odd behaviors, the more I believe that the tick-based nature of Minecraft makes things more complex than what you described. For instance, let's say you have a minecart that's at a maximum speed of 0.6 meters per tick (that's not the actual maximum, but let's just use that as an example). This minecart passes over a powered rail. Each tick the Minecraft engine increases the cart's momentum, and then moves (teleports) it 0.6 meters. If the first time the minecart was on the powered rail it was at 0.2 meters in, on the next tick it will be at 0.8 meters and it will get boosted a second time. But if the first time it was on the powered rail it was at 0.5 meters, it's only going to get boosted once.
This discrete updating, as opposed to the effectively smooth updating that we get in the real world, makes all our velocity/momentum models of minecart behavior break down if we look too closely.
Or you can just read the daniel9001 post that Xinhuan quoted.