Stopping distance

Intermediate

Distance covered while braking grows with the square of speed.

Key relationd = v²/2a

Braking distance d = v²/(2a) grows with the square of speed: double the speed means four times the distance. Total stopping distance adds the thinking distance v·t_reaction.

Worked example

At 15 m/s, 6 m/s² braking: 18.75 m. At 30 m/s: 75 m.

Common mistake

Wet roads reduce a and so increase d considerably.

In more detail

Stopping distance is the reaction distance plus the braking distance. Braking distance grows with the square of speed, so doubling your speed roughly quadruples the braking distance.

How to solve it

Split the stopping distance into two parts: the reaction distance, which is speed times reaction time, and the braking distance.
Compute the braking distance from v² = 2as with v = 0 at the end, so s = v²/(2a).
Add the two parts together.
Remember that the braking distance grows with the square of speed, while the reaction distance grows only linearly.

Worked examples

Example 1: A driver at 20 m/s has a reaction time of 0.75 s and brakes at 7 m/s². What is the total stopping distance?

Reaction distance = 20 × 0.75 = 15 m. Braking distance = 20²/(2 × 7) = 400/14 = 28.6 m. Total = 43.6 m.

Example 2: At 30 m/s, with the same reaction time and braking, what is the total stopping distance?

Reaction distance = 30 × 0.75 = 22.5 m. Braking distance = 900/14 = 64.3 m. Total = 86.8 m, about twice the first answer for 1.5 times the speed.

Checking your answer

Going from 20 to 30 m/s increases the speed by 50 percent, but the total stopping distance rises by about 99 percent. That confirms the stronger dependence on speed.

Real-world uses

Driving tests and road safety campaigns use stopping distance tables.
Vehicle designers estimate braking performance from deceleration rates.
Road safety campaigns use stopping distance to explain why doubling speed roughly quadruples the braking distance.

Open the interactive lesson, with simulation and quiz →

Frequently asked questions

Why does speed matter so much?

Braking distance is proportional to v squared, so the distance grows much faster than the speed.

What affects braking distance?

Road surface, tyre condition, vehicle mass and brake efficiency.

Why does braking distance depend on the square of speed?

Kinetic energy grows with the square of speed, and the brakes must remove all of it, so the distance grows as v squared.