well for starters, for a train to begin to move forward, it has to push backwards. (yes, I did say backwards). in doing so it is giving itself enough momentum to move, which falls under Newton's 3rd law of motion. also, since a train is on a schedule that dictates when they have to arrive at a station, they need to be able to calculate how much time it will take them to get there so they know when to leave. they can do this by knowing how far they are going to travel, their acceleration and their initial or final velocity. once they know this they can plug it into an equation to figure out how much time it should take them to get to their destination.