It's been my experience that a locked wheel will stop a car faster than one that continues to roll; exposing new rubber. As the locked wheel heats the rubber in one spot, it heats up; improving traction. Isn't that why race cars do burnouts? To heat the tires for better traction?
Lol. No sir, 100% wrong on all accounts.
A locked wheel is the slowest and most dangerous way to stop a car (since you also lose all steering ability), and physics is very clear as to why.
Traction is created by friction, and if you look up the coefficients of friction for a given material you will find there are different coefficients for different situations. The coefficient of friction for a rolling object is higher than that for a sliding object. So, a tire that is still rolling can exert more force on the ground, which means you stop faster.
Next up is the brakes themselves. Brakes stop the car by converting kinetic energy into heat. If your brakes are locked, they're not converting any motion to heat. They're stopped. So the only force acting to slow the car is coming from the tire sliding on the ground. Keep the wheel (and therefore the brakes) turning and you have both a higher coefficient of friction at the tire and also the brakes doing their job and converting motion energy into heat and dissipating it.
Then tires. Street tires and race tires have very different construction. Race tires do have better traction when they're hot, they're designed that way. They also have much shorter life spans, and are only good for a specific number of heat cycles before the composition of the tire starts to change/break down. The fancier and stickier the race tire, the fewer heat cycles they're good for. Street tires are a whole different ball game, they're designed to work over a wide range of temperatures and maintain their composition. The number of heat cycles a street tire goes through in 30k miles is enormous! So they don't see some massive improvement in traction with temperature, they can't. If they did, they'd be junk after a few thousand miles. So yeah, fancy drag race tires get a burnout to warm them up. But if you've drag raced on street tires, you should already know that a big smoky burnout is gonna make your tires slick and greasy an very little time at all. With street tires, if you do a burn out at all, it's just a VERY short one to clean the surface of debris. Anything longer is a detriment to traction. And hey, that applies to braking too! Better off keeping that tire rolling and distributing that heat.
And again, that's why ABS systems exist. It's faster to stop the car without the brakes locked, AND you can steer the car when the wheels are rolling too. Look up "threshold braking". That's the fastest way to stop a car. Unfortunately, it takes practice and skill, and since most drivers lack both of those things when it comes to a panic stop, an entire complicated system (ABS) was invented to the average driver can just slam on the pedal and have the car do the rest.
People's perception is pretty awful, your experiences will deceive you. That's why they set up complicated and regulated tests to get a real scientific answer, because it may
feel like locking up the wheels stopped you fast, but it's not the fastest way. But don't take my word for it, look up "threshold braking". You can also get great explanations is any of the Carrol Smith books, or any high performance driving class, or book, or article, or whatever. You will find exactly nowhere that a trusted source tells you that locking your brakes and sliding is the fastest way to stop.