An astronaut accidentally gets separated out of his small spaceship accelerating in interstellar space at a constant rate of $100 m{s}^{-2}$. What is the acceleration of the astronaut the instant after he is outside the spaceship? (Assume that there are no nearby stars to exert gravitational force on him)

Since there are no nearby stars to exert gravitational force on him and the small spaceship exerts negligible gravitational attraction on him, the net force acting on the astronaut, once he is out of the spaceship, is zero. In accordance with the first law of motion the acceleration of the astronaut is zero.