Is braking of a car discrete or continuous?

Answer 1

Continuous. You apply pressure on the brake pedal smoothly, and the car slows down gradually, not in jerks.

If the ABS is working, there might be an argument for the braking being discrete, since the brakes are quickly cycled on and off.

Answer 2

The answer depends on what the question is about. The braking of a car is a binary variable: either you brake or you don't. It is, therefore a discrete variable.

If, instead, the variable of interest is the time required to slow down (or stop), or the braking distance, then, since these variables can take any values (within a reasonable range), the variable is continuous. For both these variables, the application (or not) of ABS is not really relevant.