I tried to make a model for a train station that allow the minecart to stop for a few seconds but then go again, all that on a flat ground.

My solution was to have another track, next to the one used by the player, that will only serve to launch another minecart that will give momentum to the player's active minecart.

However, I found that the minecart arriving to the station won't move at all when another minecart pass on a track right next to it (see Minecart-Glitch.gif) (at least most of the time – like it's very rare it works).. The only way to make it work like this is by breaking the minecart, and placing a new one (see Minecart-Glitch2.gif)..

Powered rail below the main minecart is always properly activated by redstone, there is no difference between the two gifs, other than whether the minecart arrived of the powered rail on its own, or was manually placed there by a player).