This study focuses on the analysis of longitudinal low-speed vehicle motion, with a particular focus on jerk during starting, stopping and transient dynamics caused by braking. For this purpose a minimal vehicle model, with a body and one wheel, is developed and the corresponding dynamical system is put in a Filippov system framework to carefully capture transitions between sticking and slipping phases. Numerical simulations of the dynamical system are performed in  MATLAB, where an event-detection based approach is used to accurately determine the vehicle’s transient dynamics. The analysis reveals that the system can display stick-slip motion as well as both permanent stick and permanent slip motions. The subset of state-space where the brake is in permanent stick, which is referred to as the trapping region, is also the set where the wheel remains stationary while the vehicle body approaches a stable equilibrium. Simulations show that trajectories starting within this region also lead to smoother stops than trajectories starting outside the region since stick-slip motion lead to sudden changes in acceleration. The findings here will provide insight into how to improve ride comfort and inform how to develop new braking control strategies in automated vehicles.