Calculating the braking distance of a train is a multi-variable physics problem that is far more complex than a car's calculation due to the immense mass and lower friction of steel-on-steel contact. The basic formula is derived from the work-energy theorem: d=2⋅av2 where d is the distance, v is the velocity, and a is the deceleration rate. However, in real-world rail operations, many other factors must be included. These include the braking ratio (the force applied by the brake shoes), the coefficient of friction between the wheels and the rail (which drops significantly in rain or with fallen leaves), and the grade or slope of the track. A heavy freight train traveling at 60 mph (approx. 97 km/h) can take over a mile (1.6 km) to come to a complete stop even in an emergency application. Engineers use specialized "braking curves" that account for the time it takes for air pressure to travel through the pneumatic brake line across the entire length of the train (propagation time). Because of this, modern trains often utilize "Electronic Controlled Pneumatic" (ECP) brakes to ensure all cars begin braking simultaneously, significantly reducing the total stopping distance.