The speed you still carry when the other car has stopped
The energy of a moving car does not grow along with its speed — it grows with the square of it. Driving 25% faster does not mean 25% more energy to dissipate in a stop, it means 56% more. That gap between growing in a straight line and growing with the square is what intuition cannot see.
1. The two-car test
Two identical cars, same tires, same road. One is doing 50 mph, the other 40 mph. At the same point on the road, both slam on the brakes. The 40 mph car stops exactly at an obstacle. How fast is the 50 mph car going as it passes that same point?
2. Where your car actually stops
Total distance has two parts that grow in different ways. Reaction distance (before your foot touches the brake) grows in a straight line with speed. Braking distance grows with the square: d = v² ÷ (2·μ·g). Move the controls:
Comparison between reaction distance and braking distance as speed rises.
3. The table driving school never shows you
Total distance to a complete stop, with 1 second of reaction. The right column is the same stop in the wet, when grip drops by half:
| Speed | Dry asphalt | Wet asphalt | Same as falling from |
|---|
That last column is the most honest translation of the energy involved. Hitting a fixed obstacle at 50 mph releases the same energy as dropping from 84 feet — about an 8-story building. At 25 mph it is 21 feet: two stories. Nobody would jump from the 8th floor thinking it is "just a bit worse" than the 2nd.
4. Why the answer is 30 mph
Kinetic energy is E = ½·m·v², and the stop has to dissipate all of it. Because energy depends on v², the math is direct:
- The 40 mph car has to dissipate energy proportional to 40² = 1,600.
- The 50 mph car has to dissipate 50² = 2,500.
- Over the distance in which the first reached zero, the second shed the same 1,600. That leaves 900 — and √900 = 30 mph.
In other words: the "extra" 10 mph do not show up as 10 mph at impact. They show up as 30. And that is the optimistic case, where both brake at the same point. Give each driver 1 second of reaction and the faster car covers more ground before braking, reaching the obstacle at 35 mph.
These are idealized physics: straight-line braking, tires in good shape, uniform surface and constant deceleration. On a real road you also have vehicle load, tire temperature and wear, gradient, ABS, suspension condition and the quality of the asphalt itself. A 1-second reaction time is an average for an alert driver — fatigue, a phone or alcohol multiply it easily. Use this to grasp the order of magnitude of the risk, never as a safety margin for how close you can brake.
Work out the energy involved
Kinetic energy from mass and speed, with the formula explained.
Open the Kinetic Energy Calculator →See also: Free fall · Acceleration · Lesson: speeding saves little time