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 maximum braking capability of the host vehicle, a maximum acceleration capability of the host vehicle, and a current speed of the host vehicle; determine a current stopping distance for the host vehicle based on the current maximum braking capability of the host vehicle, the current maximum acceleration capability of the host vehicle, and the current speed of the host vehicle, wherein the maximum braking capability of the host vehicle is determined based on at least one factor associated with the host vehicle or the environment of the host vehicle; determine a current speed of the target vehicle and assume a maximum braking capability of the target vehicle based on at least one recognized characteristic of the target vehicle; and implement the planned navigational action if the determined current stopping distance for the host vehicle 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 capability of the target 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 maximum braking capability of the host vehicle, a maximum acceleration capability of the host vehicle, and a current speed of the host vehicle; determine a current stopping distance for the host vehicle based on the current maximum braking capability of the host vehicle, the current maximum acceleration capability of the host vehicle, and the current speed of the host vehicle, wherein the maximum braking capability of the host vehicle is determined based on at least one factor associated with the host vehicle or the environment of the host vehicle; determine a current speed of the target vehicle and assume a maximum braking capability of the target vehicle based on at least one recognized characteristic of the target vehicle; and implement the planned navigational action if the determined current stopping distance for the host vehicle 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 capability of the target vehicle. <EOS>