This paper addresses the issue of motion planning in dynamic environments by extending the concept of Velocity Obstacle and Nonlinear Velocity Obstacle to Acceleration Obstacle AO and Nonlinear Acceleration Obstacle NAO. Similarly to VO and NLVO, the AO and NAO represent the set of colliding constant accelerations of the maneuvering robot with obstacles moving along linear and nonlinear trajectories, respectively. Contrary to prior works, we derive analytically the exact boundaries of AO and NAO. To enhance an intuitive understanding of these representations, we first derive the AO in several steps: first extending the VO to the Basic Acceleration Obstacle BAO that consists of the set of constant accelerations of the robot that would collide with an obstacle moving at constant accelerations, while assuming zero initial velocities of the robot and obstacle. This is then extended to the AO while assuming arbitrary initial velocities of the robot and obstacle. And finally, we derive the NAO that in addition to the prior assumptions, accounts for obstacles moving along arbitrary trajectories. The introduction of NAO allows the generation of safe avoidance maneuvers that directly account for the robot's second-order dynamics, with acceleration as its control input. The AO and NAO are demonstrated in several examples of selecting avoidance maneuvers in challenging road traffic. It is shown that the use of NAO drastically reduces the adjustment rate of the maneuvering robot's acceleration while moving in complex road traffic scenarios. The presented approach enables reactive and efficient navigation for multiple robots, with potential application for autonomous vehicles operating in complex dynamic environments.