This paper characterizes safe following distances for on-road driving when vehicles can avoid collisions by either braking or by swerving into an adjacent lane. In particular, we focus on safety as defined in the Responsibility-Sensitive Safety (RSS) framework. We extend RSS by introducing swerve maneuvers as a valid response in addition to the already present brake maneuver. These swerve maneuvers use the more realistic kinematic bicycle model rather than the double integrator model of RSS. We show that these swerve maneuvers allow a vehicle to safely follow a lead vehicle more closely than the RSS braking maneuvers do. The use of the kinematic bicycle model is then validated by comparing these swerve maneuvers to swerves of a dynamic single-track model. The analysis in this paper can be used to inform both offline safety validation as well as safe control and planning.