Engineering
Vehicle stopping distance formula: reaction distance + v² / (2·μ·g) braking
Calculate thinking distance, kinetic braking distance, and total stopping distance in meters from speed (km/h), reaction time, and road friction μ.
Why doubling highway speed QUADRUPLES kinetic braking distance!
This classroom model adds constant-speed reaction travel to braking travel under constant deceleration μg on a level road. It converts km/h to m/s by dividing by 3.6.
The chosen friction values 0.75 and 0.15 illustrate sensitivity; they are not reliable coefficients for a named road condition. At90 km/h and 1.5 seconds reaction, the modeled totals are 79.97 m and 249.87 m respectively.
Actual stopping depends on tires, brakes, ABS, grade, weather, speed-dependent friction and driver response. Do not use these illustrative outputs as driving following distances or an accident-reconstruction conclusion. Doubling speed quadruples only the modeled braking term, not the combined stopping distance.
| Speed & Road Condition (t_react = 1.5 s) | Reaction Dist (v·t) | Braking Dist v²/(2μg) | Total Stopping Distance |
|---|---|---|---|
| 90 km/h (25 m/s), Dry μ = 0.75 | 37.50 m | 42.47 m | 79.97 m |
| 90 km/h (25 m/s), Ice μ = 0.15 | 37.50 m | 212.37 m (5× longer!) | 249.87 m |
| 180 km/h (50 m/s), Dry μ = 0.75 | 75.00 m (2×) | 169.89 m (4× v²!) | 244.89 m |
Total Stopping Distance (Reaction + Braking) and Braking-Only Distance in meters
Dividing A2 / 3.6 converts km/h into exact SI meters per second before applying kinematic equations.
=IF(OR(COUNT(A2:C2)<>3,A2<0,B2<0,C2<=0),"Invalid motion inputs",LET(v, A2 / 3.6, ROUND(v * B2 + (v ^ 2) / (2 * C2 * 9.81), 2)))Pure kinetic braking distance after brakes engage
Derived directly from Work-Energy equivalence: 0.5 * m * v^2 = mu * m * g * d (vehicle mass m cancels out!).
=IF(OR(COUNT(A2:C2)<>3,A2<0,B2<0,C2<=0),"Invalid motion inputs",LET(v, A2 / 3.6, ROUND((v ^ 2) / (2 * C2 * 9.81), 2)))Try the example
Use the original values or change them to test your understanding.