Problem — Fermi estimate: reaction time

Problem

Fermi estimate: reaction time on the road. Estimate the distance covered by a car at $90\;\text{km/h}$ during the reaction time of an average driver ($\sim 1\;\text{s}$).

Solution

Model. During the reaction time the driver has not yet touched the brake: the car continues at constant speed. The distance is therefore simply speed times time:

$d = v\cdot t_\text{reaz}$

Speed conversion. Recalling $1\;\text{km/h} = 1/3{,}6\;\text{m/s}$:

$v = \frac{90}{3{,}6} = 25\;\text{m/s}$

Numerical estimate. With a typical reaction time $t_\text{reaz} \approx 1\;\text{s}$:

$d = 25 \cdot 1 = 25\;\text{m}$

$\ev{d \approx 25\;\mathrm{m}}$

Twenty-five metres covered before even starting to brake: more than two buses in a row. That is the distance lost purely to human reflexes, to which the actual braking distance must then be added. This is why speed weighs so heavily on road safety.

Links

Topics: Cinematica Concepts: Velocità media Skills: Stime di Fermi