In my youth I was a big fan of space opera - rollicking tales of interstellar adventure. Of course that requires some unphysical stuff like faster than light drive, etc. I can handle that, but sometimes the details bug me.
The sliver of the Earth that had been decorating the bottom edge of the main view screen suddenly fell away from view as the ship pulled out of orbit and headed for Jupiter.
Nathan wasn’t sure if it was his gentle acceleration curve or the new inertial dampeners, but the sensation was almost unnoticeable.
In fact, it was even a bit disappointing, and he wondered how much the dampeners would help if he really had to punch it. Fifteen minutes later they were traveling at half the speed of light, and Nathan had discontinued his burn.
Brown, Ryk (2012-12-30). The Frontiers Saga: Episodes 1-3 (Kindle Locations 1518-1522). Ryk Brown. Kindle Edition.
I think a well trained pilot ought to be able to figure out that it *was* his inertial dampers. The gentlest possible acceleration curve (constant acceleration) requires that acceleration = velocity/time = 1.5 x 10^8 (m/s)/900 s or 1.7 x 10^5 m/s^2, or about 17,000 times the acceleration of gravity. Either the "inertial dampers" are working really well or the crew would be more than a bit squished.
Not counting relativistic effects, which would make it slightly worse.