Stopping distances
The total stopping distance of a vehicle has two parts:
Stopping distance = thinking distance + braking distance.
- Thinking distance — distance travelled during the driver's reaction time, while braking has not yet begun.
- Braking distance — distance travelled during braking.
Thinking distance
Thinking distance is determined by:
- Speed — at higher speed, you cover more distance in the reaction time.
- Reaction time — typically 0.5 to 1.0 s.
Increased reaction time arises from:
- Tiredness.
- Drugs/alcohol.
- Distractions (phone, conversation).
- Old age.
Braking distance
Braking distance is determined by:
- Speed — not linear. Braking distance ∝ v² (because KE ∝ v² and brakes dissipate KE).
- Mass — heavier vehicle = more KE = longer distance.
- Brake condition — worn brakes apply less force.
- Tyre condition / tread depth — affects friction.
- Road surface — wet, icy, gravel reduce friction.
✦Worked example
At 13 m/s (30 mph), thinking distance ≈ 9 m and braking distance ≈ 14 m → stopping distance ≈ 23 m. At 31 m/s (70 mph), thinking ≈ 21 m, braking ≈ 75 m → stopping ≈ 96 m.
Notice braking has grown much more than thinking — quadratic vs linear.
Why braking distance is quadratic in speed
KE = ½mv². Brakes apply roughly constant force $F$. So braking distance $s$ satisfies:
$Fs = \frac{1}{2}mv^2 \Rightarrow s = \frac{mv^2}{2F}$
Doubling $v$ quadruples $s$.
Large braking forces — risks
A sudden hard brake produces:
- Large deceleration (high g-force on driver).
- Risk of skidding (tyres lose grip).
- Possible whiplash injury.
- Brake heating — pads can lose effectiveness ("brake fade").
⚠Common mistakes
- Thinking that reaction time affects braking distance — it only affects thinking distance.
- Saying braking distance is proportional to v — it's proportional to v².
- Forgetting to add thinking + braking for total stopping.
- Confusing distance with time.
AI-generated · claude-opus-4-7 · v3-deep-physics