📖 In-Depth Theory
Stopping Distance
STOPPING DISTANCE = THINKING DISTANCE + BRAKING DISTANCE
THINKING DISTANCE: distance travelled during the REACTION TIME of the driver (before brakes are applied).
Thinking distance = speed × reaction time
BRAKING DISTANCE: distance travelled from when brakes are APPLIED until the vehicle stops.
EXAMPLE (typical values at 30 mph = 13.3 m/s):
Thinking distance ≈ 9 m
Braking distance ≈ 14 m
Stopping distance ≈ 23 m
At 60 mph: stopping distance ≈ 73 m (much more than double — braking distance increases with v²)
Factors Affecting Thinking Distance
Thinking distance = reaction time × speed
Thinking distance INCREASES with:
HIGHER SPEED — same reaction time but more distance covered.
IMPAIRED REACTION TIME due to:
ALCOHOL — slows nerve impulse transmission.
DRUGS (including some prescription medicines) — affect concentration and reaction.
TIREDNESS/FATIGUE — reduced alertness.
DISTRACTION — mobile phones, eating, passengers.
TYPICAL REACTION TIME: 0.2–0.9 seconds (average ~0.7 s).
MEASURING REACTION TIME:
Ruler drop test: drop a ruler through a person's fingers — measure how far it falls before they catch it.
Electronic reaction time testers.
Computer-based tests.
Factors Affecting Braking Distance
Braking distance INCREASES with:
HIGHER SPEED — braking distance ∝ v² (doubling speed quadruples braking distance).
POOR ROAD CONDITIONS:
Wet road: less friction between tyres and road.
Icy road: dramatically less friction.
Loose gravel: tyres lose grip.
DEFECTIVE TYRES:
Bald tyres: little tread → reduced water dispersal → aquaplaning risk.
Under-inflated tyres: reduce contact area.
POOR BRAKES: worn brake pads, overheated brakes (brake fade).
HEAVY VEHICLE: more mass → more kinetic energy to remove → longer braking distance (for same braking force).
PHYSICS LINK:
Braking force does WORK to remove kinetic energy:
Work = F × d and Ek = ½mv²
F × d = ½mv²
So d = mv² ÷ (2F)
Braking distance ∝ v² — doubling speed quadruples braking distance.
LARGE DECELERATIONS:
Hard braking → large deceleration → large forces on passengers.
Could cause injuries — seat belts and crumple zones reduce risk.
⚠️ Common Mistake
Braking distance ∝ v² — doubling speed QUADRUPLES braking distance (not doubles). Thinking distance is proportional to v (doubles when speed doubles). Students often mix up which factor affects which component.
📌 Key Note
Stopping distance = thinking + braking. Thinking distance affected by speed and reaction time (alcohol, drugs, tiredness, distraction). Braking distance affected by speed (∝v²), road conditions (wet/ice), tyre condition, brake condition, vehicle mass. Double speed → 4× braking distance.
🎯 Test Yourself
Question 1 of 2
1. A car's speed doubles from 10 m/s to 20 m/s. How does the braking distance change?
It stays the same — braking distance depends only on road conditions
It quadruples — braking distance is proportional to v², so (20/10)² = 4 times longer
It doubles — speed doubles so distance doubles
It increases by 10 m — simple addition
2. Why does alcohol increase stopping distance?
Alcohol blurs vision — the driver takes longer to see the hazard and applies brakes later
Alcohol weakens muscles — the driver cannot press the brakes as hard, increasing braking distance
Alcohol increases reaction time — the driver takes longer to respond, so thinking distance increases
Alcohol reduces vehicle mass — lighter car has less braking force available