i would think like 10 mph

According to a retired railroad brakeman of my acquaintance, there are only two speeds at which trains may operate in the U.S. -- “Maximum Authorized Speed” and “Restricted Speed.” However, several other restrictions also apply. So the answer is not a simple one. "Authorized” is the operative word. A train’s maximum authorized speed may be determined by any number of factors, including “Tons Per Operative Brake” (TPOB - total trailing tonnage divided by the number of cars), “Tons Per Axel of Dynamic Brake” (TAD - total trailing tonnage divided by the number of axles of dynamic brake), allowable track speed (determined by conditions of the roadbed), and any grade involved over the route to be used. The higher the TPOB or TAD values, the lower the authorized speed. "Restricted speed" is a speed that will permit stopping within one half the range of vision, short of any obstruction, derail, switch improperly lined, and rail separations -- not exceeding 20 MPH. There are numerous other common sense instances that can cause a train to be operated at restricted speed other than those indicated above. Furthermore, specific types of equipment have speed restrictions. If ONE of those speed restricted cars are in a train, it limits that train’s speed to the maximum at which that car can operate until the car is removed from the train's make-up. Then you have to factor in the track class, track gauge limit, whether or not the track is unsignaled or has one of two different classes of signals, whether there is a yard limit, whether the block is occupied by another train, visual restrictions, and other factors. Depending on these various criteria the speed limit may be as low as 10MPH to as high as 35MPH.

As a driver on London Underground we don't carry freight. However if you are driving an empty train (because of defect or on instruction of the emergency services (yes, they can take over a train))the maximum speed you can go through a station is 25 mph. If the station is closed however, you can only go at 5mph.