A craft with those characteristics would not only need to use some form of faster than light propulsion but also need to control the gravity from ALL directions at once instantaneously to avoid the occupants becoming grease stains on the hull from the instantaneous acceleration.
All directions? No, it just needs a very high power drive that doesn't cause the passengers to feel acceleration. Just point it in the desired direction.
That doesn't match the description of the acceleration described in the OP. And gravity is probablyn the wrong word to describe the effect.
Gravity and acceleration are synonyms in this context; Gravity is just what we call the special case of acceleration due to a nearby mass (such as a planet or star).
"Artificial gravity" is a science fiction concept, that amounts to an ability to arbitrarily accelerate the occupants of a spacecraft, such that the accelerations due to its own acceleration aren't detectable to those occupants.
The simplest solution is to rotate a spacecraft that is in free-fall, or under constant acceleration at less than that to which you wish to expose the occupants; This provides a constant acceleration
inside the vessel, without requiring constant acceleration of the vessel itself.
All other solutions are not only non-existent, but not compatible with current theories about how accelerations are caused by massive objects. We don't know exactly how gravitational forces are transmitted between masses, or even whether they are, but there's only two serious contenders:
Quantum theory suggests that these very weak forces are mediated by particles (called 'gravitons'), which are analogous to other bosons such as the photons that mediate the electromagnetic force. If so, it might perhaps be possible to block out these 'gravitons', or to generate them locally to counteract local accelerations. But quantum theory also requires that these gravitons interact very weakly with matter, and have very low or zero rest mass, and very long wavelengths (making them very difficult indeed to block), and we don't have any way to generate them in significant quantities without providing a very large mass*, which is contraindicated for an object we wish to accelerate rapidly, as this would increase our energy requirements dramatically.
Relativity, in contrast, describes gravitational acceleration as the curvature of spacetime. Artificial gravity (or antigravity, or "inertial damping") would then entail the manipulation of the curvature of spacetime, which again is something we have no theoretical way to achieve, other than by the collection of a very large amount of mass in one place.
Given the current state of our understanding of physics, we can conclude that artificial gravity, if it is possible at all, would require stupendous amounts of energy (mass and energy being interchangeable, as we know) - amounts that are simply unavailable to a small spacecraft, and which, if they could be made available, would require 100% efficiency in their use, as even a minuscule fraction of that energy, if lost as heat, would atomise any matter (including the spacecraft and its occupants) in the vicinity.
*How large? Well, to get (or counteract) an acceleration of just 1g, requires a mass of about 6x1024kg, at a distance of 6,400km. Of course, you can get the same acceleration from a smaller, but closer, mass; But then you need to start compressing your matter, and regular atomic matter requires significant effort to compress much smaller than that - if you just collect together a bunch of matter with that mass, it's own gravitational and electromagnetic forces will make it into a sphere of roughly the radius of the Earth.
The smallest size for a mass of that order (before it becomes a black hole) is a sphere of radius just under 1mm; But making it small enough to fit into your flying saucer doesn't make it any easier to accelerate. And to counteract a higher acceleration (say 10g) would require ten times the mass. And that mass would need to be itself accelerated rapidly and repeatedly, to place it in the right position relative to the occupants of the vehicle to counteract the vehicle's acceleration.
And assuming that your technology allows you to achieve all of this, tidal effects would be catastrophic, both for the spacecraft and the planet it was visiting.
