The breaking system

When the break pedal is depressed it pushes the piston in the master cylinder forward. The master cylinder pushes the break fluid through the break lines and into the slave cylinders that push the break shoes against the rotors.

The force applied by driver alone is not enough to stop the vehicle therefor the car uses mechanical systems to multiply the force. The first multiplication is mechanical advantage (leverage) by the pedal. The next multiplying step is the break booster which uses vacuum from the engine to increase the force applied. Then the hydraulic system also multiplies the the force by having the master cylinder smaller than the slave cylinders. If the master cylinder is smaller than the slave the master cylinder moves more than the slave but the slave will have more force as it has a larger surface area.

The friction between the break shoes and the rotors convert kinetic energy into heat energy. The wheels lose kinetic energy therefor the vehicle loses kinetic energy too (slows down).