If a spacecraft that seems to be emotionless in deep space is given some type of quick push what will happen

When we give a quick push to the spacecraft, we apply a force in a short time. This is equivalent to saying that we give an impulse to the spacecraft. As the momentum theorem says the impulse that we give to the spacecraft is equal to the change in its momentum
(F/\Delta t) = \Delta P
where the momentum is defined as the product between the mass and velocity.
P =mv
Therefore when we apply a quick push the speed of the spacecraft will change from zero to a constant nonzero value.

Do you have more info about it ? i doubt this is the answer because i don't have all the information but if trouble was brewing in a clinic maybe it was an argument as to which clinic was better or smth of that nature