Q.An astronaut accidentally gets separated out of his small spaceship accelerating in interstellar space at a constant rate of $100\ \text{m s}^{-2}$. 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.)

Concept: Newton's First Law (inertia in the absence of external forces)

The spaceship accelerates at $100\ \text{m s}^{-2}$ because its engines exert a thrust force. The astronaut, while inside, shares this acceleration because the ship's floor pushes on him.

The moment he separates and is outside, no force acts on him—no engine thrust, no contact with the ship, and no gravitational pull from nearby stars (given). …

Why the astronaut's acceleration becomes zero

The spaceship accelerates at $100 \, \text{m s}^{-2}$ because its engines exert a thrust force. The moment the astronaut separates, he loses contact with the ship—no floor pushes on his feet, no wall presses against his back. In deep interstellar space with no nearby stars, there is no gravitational force either.

Newton's First Law tells us that an object continues in its state of motion (constant velocity) unless acted upon by a net external force. The instant the astronaut is outside, no force acts on him. Whatever velocity he had at the moment of separation—matching the ship's velocity at that instant—he retains. But velocity staying constant means acceleration is zero.

The spaceship, meanwhile, continues to accelerate away from him because its engines keep firing.

Step-by-step reasoning

1. Identify forces on the astronaut before separation.

   While inside, the spaceship's floor exerts a normal force on the astronaut, accelerating him along with the ship at $a = 100 \, \text{m s}^{-2}$. This normal force is the only force (ignoring negligible distant stellar gravity).

2. What happens at the instant of separation?

   The contact is lost. The normal force vanishes. In interstellar space far from stars, gravitational forces are negligible. The net force on the astronaut becomes

3. Apply Newton's Second Law. $F_{\text{net}} = m a \quad \Rightarrow \quad 0 = m a \quad \Rightarrow \quad a = 0.$ …

Concept: Newton's First Law (Law of Inertia)

Step 1: Identify the forces on the astronaut while still inside the ship

Inside the ship, the floor/wall of the accelerating spaceship pushes on the astronaut, which is what gives him the same acceleration as the ship, $a_{\text{ship}} = 100\ \text{m s}^{-2}$.

Step 2: Identify the forces on him the instant he is outside

Once separated, he is no longer in contact with the ship, so there is no push/thrust force on him. The problem states there are no nearby stars, so gravitational force is also absent.

Step 3: Apply Newton's First Law

With no external force acting, $F_{\text{net}} = 0$. …