Reaction time and braking

Intermediate

Total stopping distance adds thinking distance and braking distance.

Before braking begins, the car travels at constant speed during the driver's reaction time (about 0.7 s). So total stopping distance = v·t_r + v²/2a.

Worked example

At 20 m/s with t_r = 0.7 s and a = 5 m/s²: 14 + 40 = 54 m.

Common mistake

Tired or distracted drivers have longer reaction times, which adds metres at high speed.

In more detail

Reaction time is the delay between seeing a hazard and beginning to brake, and it typically adds about 15 to 20 metres of travel at motorway speeds. Braking distance begins only after the brake is applied.

How to solve it

Identify the reaction time and the maximum distance available to stop.
Subtract the reaction distance from the available distance to find the braking distance you have left.
Use a = v²/(2s) to find the deceleration you need.
Compare the needed deceleration with what the car can actually achieve, which is usually about 7 to 8 m/s² on dry roads.

Worked examples

Example 1: A driver at 25 m/s has a reaction time of 1 s and brakes at 6 m/s². What is the total stopping distance?

Reaction distance = 25 × 1 = 25 m. Braking distance = 625/12 = 52.1 m. Total = 77.1 m.

Example 2: A driver at 20 m/s sees a hazard 50 m ahead and has a reaction time of 0.75 s. What deceleration is needed to stop in time?

Reaction distance = 15 m, so the braking distance available is 35 m. Then a = v²/(2s) = 400/70 = 5.7 m/s², which is achievable on a dry road.

Checking your answer

A deceleration of about 5.7 m/s² is well within the normal braking range, so the driver could stop in time. A required value well above what a car can achieve, such as 9 m/s² or more on a dry road, means the hazard cannot be avoided by braking alone.

Real-world uses

Road safety courses explain why keeping a larger gap to the car in front matters.
Ergonomics studies measure reaction times for control room design.
Driving instructors teach that thinking distance adds to braking distance, so the total stopping distance is longer than many drivers expect.

Open the interactive lesson, with simulation and quiz →

Frequently asked questions

What is a typical reaction time?

Often quoted as around 0.7 to 1.5 seconds, depending on alertness, distraction and age.

Can I reduce reaction time?

Not by much. Keeping a safe distance and staying alert reduces the risk more than trying to react faster.

What is thinking distance?

It is the distance the car covers in the reaction time before the brakes are applied, and it grows linearly with speed.