Rather than measuring the velocity over a short distance I would use the Hall effect switches or IR sensors, that have been suggested by others, to determine when the train is entering or leaving key sections of track. That is probably how a train driver thinks e.g 'I am at the tunnel 3 minutes ahead of normal'.
instead of having LEDs right at the track perhaps a single LED/Sensor pair in the scenery could monitor a train passing several points such as entering and then leaving a bend - that depends on track layout.
Another idea might be to have the train blow its whistle at key points e.g. entering tunnel, crossing bridge. If you could detect the whistle then you would know where the train was.