Answer:

Introduction:
The given problem is related to the motion of a rocket in a gravity-free space. The rocket is ejecting gases with a velocity of 600 m/s at a rate of 1 kg/s. We need to find out the initial acceleration of the rocket.

Explanation:
According to Newton's third law of motion, every action has an equal and opposite reaction. In the case of a rocket, the gases ejected from the rocket nozzle create a force in the opposite direction to the ejection of gases, which propels the rocket forward.

The force acting on the rocket can be calculated using the equation:

F = m * a

Where F is the force, m is the mass of the rocket, and a is the acceleration.

The mass of the rocket is given as 120 kg. The rate of ejection of gases is given as 1 kg/s, which means that after time t, the mass of the rocket will be reduced to 120 - t kg.

The velocity of the ejected gases is given as 600 m/s. According to the law of conservation of momentum, the momentum of the ejected gases will be equal and opposite to the momentum of the rocket. Therefore, the initial momentum of the rocket can be calculated as:

p = m * v

Where p is the momentum, m is the initial mass of the rocket, and v is the velocity of the ejected gases.

At time t, the momentum of the rocket will be:

p' = (m - t) * (v + u)

Where u is the velocity of the rocket.

According to the law of conservation of momentum:

p = p'

Therefore,

m * v = (m - t) * (v + u)

Solving for u, we get:

u = (m * v - t * v) / (m - t)

The force acting on the rocket can be calculated as:

F = (m * v - t * v) / (m - t)

The initial acceleration of the rocket can be calculated as:

a = F / m

Substituting the value of F, we get:

a = [(m * v - t * v) / (m - t)] / m

Simplifying the equation, we get:

a = v / (m - t)

Putting the values, we get:

a = 600 / (120 - t)

Therefore, the initial acceleration of the rocket is 5 m/s².

Conclusion:
The initial acceleration of the rocket is 5 m/s². This acceleration will decrease as the mass of the rocket decreases due to the ejection of gases.