Stopping Distance and Braking

📖 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 Equations

Stopping distance = thinking distance + braking distance

Thinking distance = speed × reaction time

Braking distance ∝ v²

📌 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.

🎯 Matching Activity — Stopping Distance Factors

Match each factor to thinking distance or braking distance. — drag the symbols on the right to match the component names on the left.

Thinking distance

Drop here

Thinking distance

Drop here

Braking distance

Drop here

Braking distance

Drop here

Both increase

Drop here

Bald tyres — less tread → reduced grip → longer distance to stop

Higher speed — thinking distance ∝ v AND braking distance ∝ v²

Wet road — reduced friction between tyres and surface

Driver is tired — reaction time increases → more distance covered before braking

Driving faster — same reaction time but higher speed → more distance

⚽ FIFA Worked Examples

Stopping Distance

A driver has reaction time 0.6 s and is driving at 20 m/s. The braking distance is 40 m. Calculate the total stopping distance.

F

Stopping distance = thinking distance + braking distance; thinking distance = speed × reaction time

I

Speed = 20 m/s, reaction time = 0.6 s, braking distance = 40 m

F

Thinking distance = 20 × 0.6 = 12 m

A

Stopping distance = 12 + 40 = 52 m

⭐ Higher Tier Only

Explain the danger of large decelerations: F = Δp/Δt — hard braking produces very large deceleration forces on passengers which can cause injury. Explain why worn tyres increase braking distance — reduced tread depth decreases water dispersal, reducing friction. Evaluate the relationship between deceleration and the risk of injury in vehicle collisions.

🎯 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?

2. Why does alcohol increase stopping distance?

⭐ How Well Do You Understand This Topic?

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Stopping Distance

Factors Affecting Thinking Distance

Factors Affecting Braking Distance

Mr. Badmus AI