252 feet or less on typical dry road in US.
The basic answer is based on US Department of Transportation minimum requirements, which requires that brakes, tires, suspension, result in a passenger car being slowed at a rate of 21 feet per second per second (21fps^2) or better. If we convert 70mph to feet per second (multiply 70 x 1.467) we get 103 feet per second. So the time it takes to stop will be 103/21, or 4.9 seconds. Using straight line deceleration this comes to 252 feet.
If everything is in good shape and typical dry road, it will take the brakes 252 feet to stop after brakes are applied. This doesn't include reaction time yet (0.4 seconds for an alert driver), as the car will travel 41 feet before he even hits the brakes. We add this to get total of 293 feet, if you include reaction time. Note that all US cars well exceed these limits, providing for a safety factor for wet roads, and other factors. You should find under ideal conditions the actual braking distance will be under 170 feet.
It takes a car 387 feet to come to complete stop when going 70mph.
If they were backing up, they would be going backwards... If they were braking, they wouldn't be going anywhere......
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A wider tire may decrease braking distance, but it depends on many factors.
A grinding noise when braking can occur when the brake pads are going bad. You are hearing the brake grinding on the metal discs.
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The technique of braking short of lockup is known as threshold braking. Modern cars have anti lock brakes to help prevent from going into full brake lockup.