Question

If a spacecraft that seems to be motionless is deep space is given some type of quick push, what will happen?

Answer 1

According to the first Newton Law of Motion (sometimes called Law of Inertia):

An object at rest or describing a uniform straight line motion (moving at constant velocity), will remain at rest or moving unless an external force is applied to it and changes its state of rest or motion.

In other words:

An object or body will keep its state of motion until an external force changes its state

This means that objects tend to remain in its state of motion, and is the definition of the inertia, as well.

Now, going back to the spacecraft in deep space of the question, if some force acts on it, the spacecraft will change its state and move in the same direction of the force applied.

It will also keep this path until another external force stops, accelerates or changes its direction.

Therefore, the right answer is C:

The spacecraft will move and will not stop until it is stopped by an equal and opposite force.  

Options A, B and D are not correct because:

A) The spacecraft cannot stop by its own; this would break Newton’s Laws of Motion

B) In deep space there is not air resistance, is vacuum.

D) The spacecraft works in space

Answer 2

I think is C 
Hope this helps ;)