Braking Distance
Distance to stop from speed v with friction μ.
Formula
Variables
Example
v=25 m/s, μ=0.7: d = 625/13.7 ≈ 45.5 m
How it works
This formula gives the idealised stopping distance due only to tire-road friction when the brakes can lock the wheels and the available friction is roughly constant. It comes from setting the work done by friction equal to the car’s initial kinetic energy, so the vehicle’s speed is reduced to zero by a constant deceleration of about μg. Because kinetic energy grows with v², doubling speed makes the braking distance about four times larger.
When to use it
Use this for rough stopping-distance calculations on level ground when you know the speed and the tire-road friction coefficient. It is common in vehicle dynamics, road safety, and physics problems that ask for the minimum braking distance under simplified conditions.
Worked example, step by step
Given: v = 20 m/s, μ = 0.8, g = 9.81 m/s² Step 1: Square the speed: v² = 20² = 400 Step 2: Calculate the denominator: 2μg = 2 × 0.8 × 9.81 = 15.696 Step 3: Substitute into the formula: d = 400 / 15.696 Step 4: Compute: d ≈ 25.5 m Final answer: The braking distance is about 25.5 m.
Common mistakes to avoid
- Using speed in km/h instead of converting to m/s first
- Forgetting that the formula gives an ideal minimum distance and ignores reaction time
- Using the wrong friction coefficient for the road surface or conditions
Did You Know?
Braking distance grows with the square of speed — doubling your speed quadruples the distance needed to stop.
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