When driving,it is vital to maintain the right following distance between the vehicles to avoid rear-end collisions. The minimum safe distance depends on many factors, however, in this study the safe distance between the human-driven vehicles and a fully autonomous vehicle at a sudden stop by an automatic emergency brake was studied based on the human driver ability to react in an accident, the vehicles braking system performance, and the speed of vehicles. For this approach, a safe distance car-following model was proposed to describe the safe distance between vehicles on a single lane dry road under conditions where both vehicles keep moving at a constant speed, and a lead autonomous vehicle suddenly stops by automatic emergency braking at an imminent incident. The proposed model then finally was being tested using MATLAB simulation, and results showed that confirmed the effectiveness of this model and the influence of driving speed and inter-vehicle distance on the rear-end collision was also indicated as well compared with the two and three seconds rule of safe following distance. The three seconds safe distance following rules is safe to be applied for all speed limits; however, the two seconds can be used on speed limits up to 45 Km/hr. A noticeable increase in rear-end collision was observed according to the simulation results if a car follows a driverless vehicle with two seconds rule above 45 km/hr.
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