Compare two speeds and friction coefficients with shared reaction time and deceleration factor. Educational constant-deceleration model, not certification of vehicle performance or safe following distance.
Parameter Settings
Scenario A: Road Preset
A: Speed v
km/h
A: Road Friction μ
Scenario B: Road Preset
B: Speed v
km/h
B: Road Friction μ
Shared Parameters
Reaction Time t
s
Deceleration Factor η
%
Stopping Distance Difference (B − A)
—
m
Live Results
Ready
Status
— km/h
A: Current Speed
— km/h
B: Current Speed
— m
A Reaction Distance
— m
A Braking Distance
— m
A Stopping Distance
— m
B Reaction Distance
— m
B Braking Distance
— m
B Stopping Distance
— m/s²
A Deceleration
— m/s²
B Deceleration
— s
Time to Stop
Braking Animation (A vs B; Reaction = Yellow, Braking = Red)
Stopping Distance vs Speed (Scenario A; Braking Grows with Speed Squared)
$v$ is in m/s (divide km/h by 3.6), $t_r$ is the reaction time [s], $\mu$ is the tire-road friction coefficient, and $\eta$ is the deceleration factor. Reaction distance is proportional to $v$; braking distance is proportional to $v^2$.
Compare reaction and braking distance under controlled conditions
This educational model assumes a level road, constant speed during reaction, and constant deceleration during braking. A and B have separate speeds and friction coefficients; reaction time and deceleration factor η are shared. It does not certify real vehicle performance or a safe following distance.
🙋
Student: If speed doubles, does the total stopping distance become four times longer?
🎓
Professor: With the same μ and η, braking distance quadruples but reaction distance only doubles. At μ=0.70, η=100% and reaction time 0.8 s, compare 60 with 120 km/h: braking is 20.2 versus 81.0 m, reaction is 13.3 versus 26.7 m. Total distance is 33.6 versus 107.7 m, not four times.
🙋
Student: What does changing η to 50% actually represent?
🎓
Professor: It halves the model deceleration a=μgη. Braking distance and braking time therefore double, while reaction distance is unchanged. η is a model factor, not a vehicle diagnostic, energy efficiency, or a calculation of ABS or regenerative-braking performance.
Equations and units
Divide km/h by 3.6 to obtain m/s. Use g=9.8 m/s² and divide the percentage input η by 100.
\(a=\mu g\eta\)
\(d_r=vt_r\)
\(d_b=v^2/(2a)\)
\(d_{stop}=d_r+d_b\)
Braking time is v/a; time from hazard recognition to rest is tᵣ+v/a. The speed sweep uses A's μ and the shared tᵣ and η. The comparison chart uses the actual A and B inputs.
Reproducible input examples
Double speed only:A=60 km/h, B=120 km/h, both μ=0.70, tᵣ=0.8 s, η=100%. A: reaction 13.3 m, braking 20.2 m, total 33.6 m. B: 26.7 m, 81.0 m, 107.7 m. Separately rounded components can differ from the rounded total by 0.1 m.
Halve friction only:Both speeds are 60 km/h; μ is 0.70 for A and 0.35 for B; tᵣ=0.8 s and η=100%. Braking changes from 20.2 to 40.5 m, total from 33.6 to 53.8 m. This is a coefficient comparison, not a measurement for a specific weather condition or tire.
Compare deceleration factors:Both scenarios use 60 km/h, μ=0.70 and tᵣ=0.8 s. Change the shared η from 100% to 50%: braking changes from 20.2 to 40.5 m, reaction remains 13.3 m. η cannot be set independently for A and B.
Assumptions, diagram and sources
Yellow indicates reaction distance and red indicates braking distance. A and B share one distance scale, fitted to the longer stop. The STOP line marks the stopping position of the illustration's left edge. Vehicle dimensions, collisions and following distance are not calculated. Distinguish animated current speed and position from the final-distance result cards.
Road slope, variable tire friction, slip ratio, ABS control, brake-force buildup, heat, regeneration and aerodynamic drag are not modeled. Surface presets are illustrative μ values. A surface name does not determine a real vehicle's μ; reaction time also depends on the person and situation. Do not use this model alone for road-safety decisions or accident reconstruction.
Braking distance starts when braking takes effect. Stopping distance also includes travel during reaction. This model calculates stopping distance as vtᵣ+v²/(2μgη).
Does doubling speed quadruple total stopping distance?
With the same μ, η and reaction time, braking distance quadruples and reaction distance doubles. The combined stopping distance generally does not quadruple. The input example compares both components.
Is η a real vehicle's brake efficiency?
Here it is a dimensionless factor in a=μgη; the percentage input is divided by 100. It is not a vehicle diagnostic or energy efficiency, and it does not calculate ABS or regenerative-braking effects.
Can the result determine a safe following distance?
Not on its own. This simplified level-road, constant-deceleration model does not reproduce actual friction, reaction, brake-force buildup or slope. Its results do not certify vehicle stopping performance or safety.
Set A and B speed and friction. Surface presets are illustrative coefficient values.
Set the shared reaction time and deceleration factor η. Divide its percentage by 100.
Compare the diagram, speed sweep and A/B components. Example buttons change only speed, friction or the shared factor.
Run and reset control animation time. Reset does not restore initial parameter values.
Check identical conditions
At μ=0.70, η=100%, reaction time0.8 s:60 km/h gives reaction13.3 m, braking20.2 m, total33.6 m. At120 km/h:26.7 m,81.0 m,107.7 m. Independently rounded components may differ from the total by0.1 m.
Model limitations
Level road and constant deceleration; no slope, ABS, real tire model or regeneration.
η scales model deceleration; it is not a measurement of vehicle maintenance or energy efficiency.
Reaction time and friction cannot be uniquely inferred from a situation or surface name.
The model does not certify road-design compliance, actual vehicle stopping performance or safe following distance.