When driving on slick roads why is it advisable to apply the break slowly?

If you apply the breaks quickly on a slick road, the wheels' rotational movement will come to a complete stop, but the car itself will keep moving forward, causing the car to slip. It happens because the force of friction, Ff, is small. The traction of the wheels on the ground (which requires that the wheels continue to roll at the speed that the ground moves past them, which is what normally happens) is what allows the driver to maintain control of the car. If the wheels suddenly were not gripping the ground, which would happen if their rotational motion stopped, the driver would have not control over the car.

Slowly applying the breaks is advised because the force of friction is not exceded by the force of the breaks. In otherWords, friction (traction) still causes the wheels to roll, mainting the driver's control over the car. If the force of the breaks exceeds that of friction, then the wheels will come to a stop before the car does.