An astronaut accidentally gets separated out his small spaceship accelerating in interstellar space at a constant rate of `100ms^(-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 gravitional force on him)

Options

A. zero
B. `10ms^(-2)`
C. `50ms^(-2)`
D. `100ms^(-2)`

Explanation

To solve the problem, we need to analyze the situation of the astronaut who has just separated from the spaceship.

### Step-by-Step Solution:

1. **Understanding the Situation**:
The astronaut is initially inside a spaceship that is accelerating at a rate of \(100 \, \text{m/s}^2\). This means that the spaceship is applying a force on the astronaut, allowing him to accelerate along with it.

**Hint**: Consider the forces acting on the astronaut while he is still inside the spaceship.

2. **Applying Newton's Laws**:
According to Newton's second law, the acceleration of an object is determined by the net force acting on it divided by its mass (\(F = ma\)). When the astronaut is inside the spaceship, the force exerted by the spaceship results in the astronaut accelerating at \(100 \, \text{m/s}^2\).

**Hint**: Recall that the astronaut's acceleration is due to the force exerted by the spaceship.

3. **Separation from the Spaceship**:
When the astronaut separates from the spaceship, he is no longer under the influence of the force exerted by the spaceship. In interstellar space, there are no other forces acting on him (assuming no nearby gravitational forces).

**Hint**: Think about what happens to the forces acting on the astronaut once he is no longer in contact with the spaceship.

4. **Determining the Acceleration**:
Since there are no forces acting on the astronaut after he separates from the spaceship, according to Newton's first law (an object in motion stays in motion with the same speed and in the same direction unless acted upon by a net external force), the astronaut will not experience any acceleration.

**Hint**: Remember that in the absence of external forces, the acceleration of an object is zero.

5. **Conclusion**:
Therefore, the acceleration of the astronaut the instant after he is outside the spaceship is \(0 \, \text{m/s}^2\).

**Final Answer**: The acceleration of the astronaut is \(0 \, \text{m/s}^2\).