Since the problem is usually done with a trolley, and trollies are much lighter than trains, I have reason to believe I might stop the trolley, or at least slow it down enough to keep it from injuring the people further down the track. However, if there is any debris in the vicinity, I would throw that first.
Though, with Project: Immovable and Project: Barricade, I might be able to stop it without dying.
Who knows? I might be a very convincing artificial intelligence.