There is a moment in time when the speed of the decelerating train coming to a halt matches perfectly the speed of my person walking on the platform towards the soon-to-open doors. My speed is constant while the deceleration of the train is constant in that it approaches zero. There is a fraction of a second, a sliver really according to a delta function in time, when the passenger to the left looking outside of the window could be sitting in a stationary train with me standing still, but this is not so. It is an illusion of movement. One object slowing down and the other looking for an entrance which will slide open with a pumping sound of air exuding.

Um. I'm sorta confused....

Okay, I will attempt to reword this more clearly. As the train slows down to a stop, I walk along the platform to get in. At some point in time, the movement of the train in relation to me is zero because the speed I am walking matches the speed of the train. Even though we are both moving, because we are at the same speed it seems to me and the passenger in the train that we are not moving in relation to each other. Kind of like when you are on the highway passing another car which is slowing down. Is this more clear?

It is sort of akin to certain motion picture cinematography tricks. You see a lot of motion going on relative to the person moving fast (so that you know that the subject is moving fast). As the person slows down, the motion around seems to slow down as well. Then as that person approaches a stop, the other motion that had been zooming by in one direction is now moving at normal rates in their appropriate directions relative to the ground (no longer soley relative to the person that is moving). This is a difficult concept to visualize at first.

Sometimes when the train stops and I look up from the book I am reading to look outside, it seems like the train is still moving because the landscape has the illusion of movement. Similar to swimming all day in the ocean and lying in bed that evening with the motion of the waves still tossing your body back and forth. At least it feels that way.

Yes, that is much clearer. I thought that was what you were saying, but I wasn't too sure. Thanks, Kiff.

Alright Bek now you know for sure. I will try to write more clearly and down-to-earth in the future. But that is difficult for me as you can guess.