Reaction time and thinking distance
Reaction time is the time between seeing a danger and starting to brake. For an alert driver it is about 0.7–1 s.
During this time the vehicle does not slow down. The distance covered is the thinking distance:
thinking distance = speed × reaction time (speed in m/s, time in s).
Change km/h to m/s by dividing by 3.6. Example: 50 km/h ÷ 3.6 ≈ 13.9 m/s. With 1 s reaction time the car moves about 14 m before braking even starts.
What makes reaction time longer: using a phone, tiredness, alcohol or drugs, loud music, talking a lot. A phone call can double reaction time.
Braking distance and stopping distance
After the brakes are pressed, the vehicle slows down at a rate called deceleration (a, in m/s²). On a dry road a good car can slow at about 7 m/s².
braking distance = v² ÷ (2a)
Because speed is squared, doubling speed makes the braking distance 4 times longer; tripling it makes it 9 times longer.
stopping distance = thinking distance + braking distance
| Speed | Thinking (1 s) | Braking (dry) | Stopping |
|---|---|---|---|
| 30 km/h | 8 m | 5 m | 13 m |
| 50 km/h | 14 m | 14 m | 28 m |
| 100 km/h | 28 m | 55 m | 83 m |
The braking force comes from friction between tyres and road. Heavier loads, worn brakes or bald tyres also make braking longer.
Grip, wet roads and bends
Grip is the friction between tyres and road. When a wheel rolls without sliding, it is static friction that pushes the car.
- Wet road: grip falls to about half. Icy road: grip is tiny. Braking distance grows a lot.
- Bald (smooth) tyres cannot push water away, so the car may slide on water (aquaplaning).
On a bend the car needs a sideways force toward the centre of the curve (centripetal force). Only friction gives it. The tighter the bend (small radius) or the faster the car, the more grip is needed: vmax = √(μ g r), where μ is the grip number (about 0.7 dry, 0.4 wet), g = 9.8 m/s² and r is the radius.
If the car is too fast, it slides outward. Tall vehicles (buses, trucks) can also tip over. Slow down before the bend, not in it. Roads are sometimes tilted (banked) to help.
Impact safety: seat belts, helmets, airbags and crumple zones
In a crash the body is moving and must stop. By Newton's laws, force = mass × change in velocity ÷ time (F = m·Δv/Δt). The change in velocity is fixed by the speed, so the only way to lower the force is to make the stopping time longer.
- Seat belt: holds you, stretches a little, spreads the force over chest and hips. Without it, inertia throws you forward into the dashboard or out of the car.
- Airbag: a soft cushion that slows the head over a longer time.
- Crumple zone: the front and back of the car squash on purpose, taking longer to stop.
- Helmet: hard shell spreads the blow; soft foam inside squashes and adds time.
- Child seat: small children need a seat that fits them.
Safe as a pedestrian, passenger, cyclist and scooter rider
- Pedestrian: use crossings and footpaths; stop, look both ways, listen; never cross from behind a parked bus; wear light or reflective clothes at night; no phone while crossing.
- Passenger: always wear the seat belt, front and back; do not distract the driver; get out on the footpath side.
- Cyclist: helmet, lights (white front, red back), bell, working brakes; ride in the direction of traffic; give hand signals; keep both hands ready; stay visible.
- E-scooter / moped rider: helmet, one person only, obey the local age and speed rules, no footpath riding where not allowed.
- Bus, train, tram: wait behind the line, hold the handrail, never get on or off a moving vehicle.
Traffic lights and signs are a shared language: red = stop, amber = get ready to stop, green = go if safe.
After an accident, and safe, sustainable mobility
If you see an accident: keep yourself safe first; warn other traffic; call the emergency number (112 in India and Europe); do not move an injured person unless there is fire or other danger; stop heavy bleeding with firm pressure; keep the person warm and talk to them until help comes.
Safe, sustainable mobility means getting around in ways that are safe, healthy and clean: walking, cycling, buses and trains. Streets are public space shared by everyone. Cities make them safer with footpaths, cycle lanes, speed limits of 30 km/h near homes and schools, speed bumps and good lighting.
Key formulas and definitions
- speed in m/s = speed in km/h ÷ 3.6
- thinking distance = v × t (reaction)
- braking distance = v² ÷ (2a)
- stopping distance = thinking distance + braking distance
- maximum speed on a bend: v = √(μ g r)
- impact force: F = m·Δv / Δt (longer Δt → smaller F)
Worked examples
1. A car moves at 36 km/h. The driver's reaction time is 0.8 s. Find the thinking distance.
36 ÷ 3.6 = 10 m/s. Thinking distance = 10 × 0.8 = 8 m.
2. A car at 20 m/s brakes with a deceleration of 8 m/s². Find the braking distance.
Braking distance = v² ÷ (2a) = 400 ÷ 16 = 25 m.
3. A scooter at 54 km/h; reaction time 1.2 s; deceleration 5 m/s². Find the stopping distance.
v = 54 ÷ 3.6 = 15 m/s. Thinking = 15 × 1.2 = 18 m. Braking = 225 ÷ 10 = 22.5 m. Stopping = 40.5 m.
4. A car's braking distance at 40 km/h is 9 m. Estimate it at 80 km/h on the same road.
Speed doubles, so braking distance × 2² = 4. 9 × 4 = 36 m.
5. How fast can a car safely take a bend of radius 50 m on a dry road (μ = 0.7)? And on a wet road (μ = 0.4)? Use g = 9.8 m/s².
Dry: v = √(0.7 × 9.8 × 50) = √343 ≈ 18.5 m/s ≈ 67 km/h. Wet: v = √(0.4 × 9.8 × 50) = √196 = 14 m/s ≈ 50 km/h.
6. A 60 kg passenger goes from 15 m/s to 0. With a seat belt the stop takes 0.3 s; hitting the dashboard it takes 0.02 s. Compare the forces.
With belt: F = 60 × 15 ÷ 0.3 = 3000 N. Dashboard: F = 60 × 15 ÷ 0.02 = 45 000 N, which is 15 times larger.
Common mistakes
- Using km/h directly in v × t or v²/(2a). Always change to m/s first (÷ 3.6).
- Thinking that double speed means double braking distance. It is four times, because v is squared.
- Forgetting the thinking distance. The car does not slow at all during the reaction time.
- Believing a seat belt or helmet 'stops the crash'. It works by making the stop longer, so the force is smaller.