How far your car travels before it stops depends heavily on speed - and not in a straight line. Understanding this relationship is key to safe following distances. Here is how stopping distance changes with speed.
It grows with the square of speed
The braking portion of stopping distance increases with the square of your speed. That means doubling your speed roughly quadruples the distance needed to stop - going from 30 to 60 mph does not double the stopping distance, it multiplies it about four times.
Reaction distance adds to it
Total stopping distance is reaction distance (how far you travel before you hit the brakes) plus braking distance. Reaction distance grows in a straight line with speed, but the braking part grows much faster, so high speeds are disproportionately dangerous.
Conditions matter too
Wet, icy, or worn-tire conditions lengthen it further - the brakes can only stop the car as well as the tires grip; see wet braking and tires and braking. Hot, faded brakes also stretch the distance; see brake fade.
The safety takeaway
Leave more following distance than feels necessary at higher speeds, and keep the brakes and tires in good shape so you get the shortest stop possible; see when to replace pads. Fit quality pads and hardware.