Why do the fast trains take a mile and a quarter to stop in a emergency stop?
Because they got bald steel tyres running on steel rails, these trains actually stop pretty well 125 to 0 in 1.25 miles even if uk HST s are nearer 700 feet long than 8000. There is a huge amount of nonsense above about slow acting brakes, the old railway companies used slow acting brakes pre war , 1st War Great Western, 2nd the others, and Mallard was engaged in brake tests testing much the same brakes city of Truro had in 1904, newly introduced on to the LNER , when it achieved the world speed record of 126 MPH on 3rd Juy 1938. HSTs and MK 3 and 4 coaches use disc brakes but it is the lack of adhesion between rail and wheel which limits braking.
Actually the fast trains also have electronic controlled brakes, that react a lot faster. Some high speed trains have as many as four disk brake rotors per axle, and some have eddy-current or magnetic brakes, powerful electromagnets against the rail which develop retarding force, as well as create magnetic force which adds to gravity to create a greater normal force and allow more braking without skidding wheels. But most of all, Energy is Mass times Velocity Squared. The higher the speed, exponentially more effort is required to retard it. And, no one asks why it takes them so long to get at that speed in the first place. That’s why they limit the number of stops high speed trains stop at. It takes a while to slow down and speed back up.
