[tsimionescu]

Your explanation would lead to the 0.5s answer - that's how long it takes for the first signal to ripple through the wires.

To get the 1m/c s answer, for your example you would have to add a seismograph to the opposite end of the train track - while the cart at that far end will only start moving once the ripple goes around the whole track, the seismograph will pick up the movement almost instantly, since the movement of the initial cart will send waves through the earth directly, not following the tracks.