When the rail beds were engineered, what speeds were they designed to accommodate? How do the new trains deal with existing curves of the rails?
Well, the Pennsylvania Railroad ran electrics at around 100 mph since the 1930s; they were the fastest railroad between New York and Washington even back then, faster than the competing Baltimore and Ohio, which went to Jersey City instead of Manhattan. They did accelerate a bit slower than the modern trains, mostly due to having twenty cars behind a 4400-horsepower electric engine, and the fastest time was about 3½ hours one-way between the two cities. And of course, the rails back then were all jointed, versus today’s continuous welded rails.
The Acela Express is a tilting train, which means that it is supposed to be able to go through curves faster than a non-tilting train; that is to say, non-tilt trains can go around curves faster than they are rated to but they are held to a certain speed so that passengers will stay in their seats and not get nauseous, which is something that tilting suspensions are supposed to help overcome. Thanks to the Federal Railroad Administration stipulating added weight to improve frontal (primarily) crashworthiness (1.8-million pound frontal impact), the tilt angle had to be cut back from 9° cant deficiency to somewhere between 4° and 5°, which eliminates the advantage of a tilt train. Furthermore, Metro-North Railroad and Connecticut DOT has prohibited Amtrak from using the Acela’s active-tilt system, citing track centers that are too close together for the width of trains for fear of trains sideswiping each other (Acela is 10’ 4” wide and the non-tilting commuter cars of Metro-North are 10’ 6” wide).
The main excuse for not running faster than 125 mph on the former Pennsylvania Railroad even to this date was and is the legacy overhead wires, which are variable-tension (they change tension with changes in atmospheric pressure, which means they sag in hot weather). The federal government has been promising funding to convert the wires to constant tension (a weight and pulley system that keeps the wires at a certain tension no matter the ambient temperature), but of course they have been promising this for decades now, and when the Budd Metroliner first came out, this was not even an issue cited that I can recall (or see in documentation) preventing operation at 160 miles per hour.