Systems and methods are provided for vehicle navigation. In one implementation, a system for a host vehicle includes at least one processor programmed to determine, based on an output of at least one sensor of the host vehicle, one or more target dynamics of a target vehicle; determine, based on one or more host dynamics of the host vehicle and the target dynamics, a time to collision; determine, based on the time to collision and the host dynamics, a host deceleration for the host vehicle to avoid the collision; determine, based on the time to collision and the target dynamics, a target deceleration for the target vehicle to avoid the collision; determine, based on the host deceleration and the target deceleration, a host deceleration threshold; and determine, based on a speed of the host vehicle and the host deceleration threshold, to brake the host vehicle.