Describing Motion Around Us
Stopping distances and safety
Find out why a little more speed means a much longer stopping distance.
The real question. On the highway, a truck is in front of you. How far behind it should you stay? Physics can answer this, and the answer may surprise you.
Braking distance. Once the brakes are on, the car slows down and stops. Use v² = u² + 2as with v = 0 (the car stops). Then s = u² ÷ (–2a). With brakes giving a = –4 m s⁻², that is s = u² ÷ 8.
- At 54 km h⁻¹ (15 m s⁻¹): 225 ÷ 8 ≈ 28.1 m.
- At 108 km h⁻¹ (30 m s⁻¹): 900 ÷ 8 = 112.5 m.
Double the speed, four times the distance. The speed is squared in the formula. Twice the speed means 2 × 2 = four times the braking distance. A small push on the accelerator makes a big difference when you need to stop.
First you have to react. Before the brakes work, the driver has to see the danger and press the pedal. During that reaction time, the vehicle keeps going at full speed. So:
stopping distance = reaction distance + braking distance.
The bus and the obstacle. A bus at 10 m s⁻¹ sees an obstacle 30 m ahead.
- The driver takes 0.5 s to react: 10 × 0.5 = 5 m.
- The brakes (a = –2.5 m s⁻²) stop it in 10² ÷ (2 × 2.5) = 20 m.
- Total: 5 + 20 = 25 m, so it stops 5 m before the obstacle.
What makes stopping take longer:
- higher speed;
- a wet or slippery road;
- weaker brakes;
- a slower reaction (a tired or distracted driver).
So keep a safe gap from the vehicle in front, and make it bigger when you go faster.
Journeys in stages. Work out each part separately, then add: speed up from 0 to 20 m s⁻¹ in 5 s (50 m), go steady for 10 s (200 m), brake to a stop in 6 s (60 m). Total: 310 m.
Technology that helps. Vehicle-to-vehicle (V2V) communication, being developed in many countries including India, lets vehicles send signals to each other and warns drivers of a possible crash.
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