Inertia without Mystery: Forces in Non-Inertial Frames and the Inertial (Fictitious) Term

Introduction: As a bus brakes, the passengers experience a forward force that can be described by Newton's second law in both inertial and non-inertial frames. This is an important effect essential to explaining motion in common scenarios.
Objectives: It aims to measure the influence of braking, such as the inclination of the effective vertical and friction thresholds, and the relative displacement during slip, and also investigate the influence of braking profiles on comfort.
Methods: The study computes the translational frame transformation, introduces the effective-gravity vector, and examines braking dynamics using piecewise and jerk-limited braking profiles.
Results: The analysis provides quantitative estimates of tilt, friction limit, and slip dynamics, as well as an
understanding of the correlation between braking profiles and passenger comfort.
Conclusions: This framework offers a replicable analytical approach for explaining and anticipating the physical impact of braking on passengers.

Originally published in Letters in High Energy Physics on 2026-02-14. This Zenodo record archives the published article as a repository copy.