Braking Distance Physics: Twice the Speed = 4× the Distance

Step by step

1. Twice the speed → 4 × as far to stop. Why?
   Drive twice as fast, and your car needs four times as far to stop. Why four times?
2. 20 mph → 6 m · 40 mph → 24 m · twice the speed, 4 × the distance
   At twenty miles an hour, a car brakes in about six meters. At forty, it needs about twenty-four meters. Twice the speed, four times the distance!
3. Most people guess 2 × → 12 m ✗ · it's 24 m. Why?
   These are UK Highway Code numbers. Most people guess that twice the speed means twice the distance: twelve meters. So why twenty-four?
4. Deceleration: brakes take away speed bit by bit, at a steady rate
   The key idea is deceleration. Brakes don't stop a car at once. They take away its speed bit by bit, at a steady rate.
5. Easy numbers: − 10 mph every second
   For easy numbers, say the brakes take away ten miles an hour every second.
6. 20 → 10 → 0: 2 s · 40 → 30 → 20 → 10 → 0: 4 s
   From twenty: twenty, ten, zero. It stops in two seconds. From forty: forty, thirty, twenty, ten, zero. Four seconds.
7. Time × 2: the first doubling
   So the faster car brakes for twice as long. That's the first doubling, and it's where most people stop.
8. Average speed: 20, not 10 → the second doubling
   But during those seconds, it's also moving faster. Its average speed while braking is twenty, not ten. That's the second doubling.
9. Distance = average speed × time: 10 × 2 = 20 · 20 × 4 = 80 → 4 ×
   Distance is average speed times time. Ten times two is twenty. Twenty times four is eighty. Eighty is four times twenty!
10. Width = time, height = average speed · double both → 4 boxes
    On a speed graph, time is the width, and average speed is the height. Double both, and four small boxes fill the big one.
11. Any steady rate: 2 × 2 = 4
    Any steady braking rate gives the same result. Twice the speed: two times two, four times the distance.
12. Speed × 2 → distance × 4 · speed × 3 → distance × 9
    So braking distance grows with the square of the speed. Three times as fast? Three times three: nine times as far.
13. On a test: time × 2, average × 2 → distance × 4 → 24 m
    On a test, write it like this. Twice the speed means twice the braking time, and twice the average speed. Distance is average speed times time, so it's four times as far: twenty-four meters.