What is Braking Distance?
Braking distance is the distance a vehicle travels from when the brakes are first applied until it comes to a complete stop. It depends on the vehicle's velocity, the road surface, and the effectiveness of the brakes—and it increases with the square of velocity.
Braking distance is calculated as s = v² / (2 × a), where v is velocity (m/s) and a is deceleration (m/s²). Doubling speed quadruples braking distance.
Try it: interactive calculator
Step-by-step worked examples
A car is traveling at 20 m/s when the driver applies the brakes with a deceleration of 5 m/s². What is the braking distance?
v = 20 m/s, a = 5 m/s² s = v² / (2a) s = (20)² / (2 × 5) s = 400 / 10 s = 40 metres
If the same car doubles its speed to 40 m/s (with the same deceleration of 5 m/s²), what is the new braking distance?
v = 40 m/s, a = 5 m/s² s = (40)² / (2 × 5) s = 1600 / 10 s = 160 metres Note: 40 m → 160 m is a 4× increase despite only 2× speed increase.
On wet roads, deceleration drops to 3 m/s². At 15 m/s, what is the braking distance?
v = 15 m/s, a = 3 m/s² (wet road) s = (15)² / (2 × 3) s = 225 / 6 s = 37.5 metres Wet roads require 50% longer stopping distance than dry roads (compare: 15 m/s on dry = 22.5 m).
Flashcards
Quick quiz
Q1.A vehicle at 10 m/s decelerates at 5 m/s². Braking distance:
Q2.Speed triples from 10 m/s to 30 m/s (same deceleration). Braking distance multiplies by:
Q3.Wet road (a = 3 m/s²) vs dry (a = 6 m/s²) at 20 m/s:
Q4.Tired brakes reduce deceleration to 3 m/s² instead of 5. At 18 m/s, extra distance needed:
The full card deck, worked steps and AI-tutor support for “What is Braking Distance?” are in Notek — study by hand before your exam.
Common mistakes
Braking distance increases linearly with speed (double speed = double distance). — Correct: Braking distance grows with v², so doubling speed quadruples distance.
Wet roads increase braking distance by about 20–30%. — Correct: Wet roads typically increase braking distance by 40–70% depending on conditions.
Braking distance is the same regardless of how heavily you press the brake pedal. — Correct: Harder braking increases deceleration, reducing stopping distance—better brakes and tires = lower distance.
At 100 km/h on a highway, braking distance is about 50 m. — Correct: 100 km/h ≈ 27.8 m/s; with a = 5 m/s², distance ≈ 77 m. Higher speeds demand far more distance.
FAQ
What is the braking distance formula?
s = v² / (2a), where s is braking distance (m), v is velocity (m/s), and a is deceleration (m/s²).
Why does speed have such a large effect on braking distance?
Because kinetic energy is proportional to velocity squared (½mv²). Doubling speed quadruples the energy that brakes must dissipate.
What deceleration should I assume for typical dry asphalt?
Approximately 5–7 m/s² with good brakes and tires. Wet roads: 3–4 m/s². Ice: 1–2 m/s².
How much longer is braking distance in wet conditions?
Typically 40–70% longer than dry conditions, depending on surface water depth and tire tread. Assume deceleration drops to 3 m/s² on wet roads.