Due to the development of advanced driver assistance systems (ADAS) and autonomous vehicle (AV) technology, various path planning algorithms are being developed. However, most path planning algorithms operate in general and safety scenarios, and in emergency scenarios, the autonomous emergency brake (AEB) and autonomous emergency steering (AES) systems are operated limitedly. In an emergency situation in which the vehicle dynamic characteristics changed, planning a safe trajectory that can be safely tracking in necessary. In this study, a safe trajectory planning method in which the vehicle does not lose stability by using combined longitudinal and lateral acceleration vectors is proposed. The combined acceleration vector is limited by friction limit. The proposed trajectory planning algorithm is evaluated by simulation in a single obstacle scenario through comparison with existing AEB and AES algorithms. The simulation results show the proposed algorithm generates only safe trajectory that guarantee the vehicle stability, excluding dangerous trajectories when the AEB and AES algorithms operated.