# Why a car stops slower when you press the brake pedal fully rather than progressively?

I have always been told that if you press the brake pedal fully and fast it can make the wheels lock themselves, and that you shouldn't do so because it would take longer to stop the car than if you push the brake pedal progressively, why so?

I can imagine that when done progressively the car won't start doing jumps due to the wheels block as if you would brake immediately but I can't see why.

• physics.stackexchange.com/a/69947/291677 "there is energy dissipation only if there is motion with (kinetic) friction creating a resisting force" Commented Aug 18, 2023 at 12:07
• the brakes stop the wheels, the tires on the wheels stop the car. Commented Aug 18, 2023 at 18:29
• en.wikipedia.org/wiki/Rolling_resistance Commented Aug 19, 2023 at 1:07

I assume you are referring to a car without ABS brakes.

If the wheels lock, then the wheels skid, and the friction force exerted by the ground on the wheels slowing the car down changes from static friction to kinetic (sliding) friction. This is because hard braking may result in the wheel exerting a force on the ground that exceeds the maximum possible opposing static friction force.

Since the kinetic friction force is generally lower than the static friction force just prior to skidding, it would take longer to stop with kinetic friction than static friction.

Hope this helps.

• why would a wheel that is rotating slower (by pushing progressively the brake) have static friction force and the wheel that is sliding or stopping (by pushing fully the brake) have kinetic friction force? Commented Aug 18, 2023 at 12:45
• @Ulshy Whether the wheel is rotating or not, it is the friction force that the road applies backwards on the wheel that is responsible for decelerating (slowing) the car . It is the only external force (ignoring air resistance and rolling resistance)opposing the motion of the car. If you progressively increase the braking force, and do not exceed the maximum possible static friction force, you progressively increase the static friction force for a more controlled braking. Commented Aug 18, 2023 at 13:49
• But regardless of whether the braking is progressive or sudden, if the braking force exceeds the maximum possible static friction force , the wheel skids as friction changes from static to the lower kinetic friction force and deceleration decreases. Commented Aug 18, 2023 at 13:49
• @Ulshy: Think of it this way: If you slam on the brakes, then the wheels stop spinning at all, and the car then slides. If the care is sliding, then it is not stopping. If you only hit the brakes 80% of the way, then the tires can push hard against the road the entire time. Commented Aug 18, 2023 at 20:41
• Try sliding something heavy on a floor, or something less heavy on a table top. The initial force required to start it in motion is greater than that required to keep it in motion. You could test this using a spring. You will find that the object will 'scoot' a short distance across the table top once static friction is overcome without you moving the other end of the spring. Commented Aug 18, 2023 at 21:45

# It doesn't

The car will stop in the shortest distance when the maximum effective braking force (the maximum force which does not result in slip) is applied as quickly as possible. However, most humans are not able to determine this maximum force analytically under dynamic conditions, so applying the brakes with progressive force allows them to sense the onset of skid conditions without solving an impossibly difficult set of dynamic equations in milliseconds.

Anti-lock braking systems do not attempt to compute the maximum braking force at all. They simply allow the brakes to exceed it, and then quickly release them once skid conditions are detected. This is less effective than applying the maximum force continuously, but the difference is small enough to not matter (i.e., computing the maximum force explicitly and building a control system that can use this information precisely is too expensive to justify).