1. Physical Mechanics of Deceleration

1. Physical Mechanics of Deceleration

From the Work-Energy Theorem in physics, the kinetic energy dissipated during friction braking is: $\Delta E_k = \frac{1}{2} m v^2 = F_f \cdot d$

where $F_f = \mu m g$ is the tire-road frictional force. Therefore: $d_{\text{friction}} \propto v^2$

Combining this with the human driver reaction distance $d_{\text{reaction}} = v \cdot t_{\text{reaction}}$ yields the composite stopping model: $d(s) = \alpha s^2 + \beta s$

where $s$ is the vehicle speed in $\text{km/h}$.