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.