A system for navigating a host vehicle, the system comprising: at least one processing device programmed to: receive, from an image capture device , at least one image representative of an environment of the host vehicle; determine, based on at least one driving policy, a planned navigational action for accomplishing a navigational goal of the host vehicle; analyze the at least one image to identify a target vehicle in the environment of the host vehicle; determine a next-state distance between the host vehicle and the target vehicle that would result if the planned navigational action was taken; determine a current speed of the host vehicle; determine a current speed of the target vehicle and assume a maximum braking rate capability of the target vehicle based on at least one recognized characteristic of the target vehicle; and implement the planned navigational action if, for the determined current speed of the host vehicle and at a predetermined sub-maximal braking rate, or for the determined current speed of the host vehicle and for a predetermined braking rate profile, the host vehicle can be stopped within a host vehicle stopping distance that is less than the determined next-state distance summed together with a target vehicle travel distance determined based on the current speed of the target vehicle and the assumed maximum braking rate capability of the target vehicle, wherein: the predetermined sub-maximal braking rate is less than a maximum braking rate capability of the host vehicle; and the predetermined braking rate profile progressively increases from a sub-maximal braking rate to a maximal braking rate for the host vehicle. receive, from an image capture device , at least one image representative of an environment of the host vehicle; determine, based on at least one driving policy, a planned navigational action for accomplishing a navigational goal of the host vehicle; analyze the at least one image to identify a target vehicle in the environment of the host vehicle; determine a next-state distance between the host vehicle and the target vehicle that would result if the planned navigational action was taken; determine a current speed of the host vehicle; determine a current speed of the target vehicle and assume a maximum braking rate capability of the target vehicle based on at least one recognized characteristic of the target vehicle; and implement the planned navigational action if, for the determined current speed of the host vehicle and at a predetermined sub-maximal braking rate, or for the determined current speed of the host vehicle and for a predetermined braking rate profile, the host vehicle can be stopped within a host vehicle stopping distance that is less than the determined next-state distance summed together with a target vehicle travel distance determined based on the current speed of the target vehicle and the assumed maximum braking rate capability of the target vehicle, wherein: the predetermined sub-maximal braking rate is less than a maximum braking rate capability of the host vehicle; and the predetermined braking rate profile progressively increases from a sub-maximal braking rate to a maximal braking rate for the host vehicle. the predetermined sub-maximal braking rate is less than a maximum braking rate capability of the host vehicle; and the predetermined braking rate profile progressively increases from a sub-maximal braking rate to a maximal braking rate for the host vehicle. <EOS>