In the movie The Wandering Earth, the rotation of Earth is slowed to a stop, and then 10000 engines are strapped to one side of the planet and used to accelerate it out of the solar system. The plot also involves slingshotting around Jupiter, but this doesn't really matter for the purposes of this question.
I found a somewhat related question on Astronomy, however this deals with acceleration due to gravity. In essence it states that if a planet accelerates due to gravitational forces (e.g. an eccentric orbit around a star), everyone and everything on the planet is also being accelerated by the same source and thus the acceleration wouldn't seem to affect anything.
I considered asking this question on Astronomy, however the question asking guide there seems to indicate that any hypothetical scenarios should be asked here. Similarly the Movies SE site doesn't seem like an appropriate place to ask this type of question.
If a planet was accelerating due to engines on its surface, people on the planet should (in theory) be able to feel that acceleration, since they aren't being pushed by the engines, only the planet they're on is. I would imagine that if the acceleration wasn't significant it wouldn't really be noticeable, however if this acceleration was high enough (e.g. more than 1G) then would the people on the rear side of the moving planet actually fall off? Would the atmosphere of the planet counteract some of these forces in any way or would that be stripped off the planet as well?
This question isn't about the mechanics or realism of strapping engines to a planet and moving it. I looked up a few similar questions on the site (e.g. here and here), and although they do highlight some of the possible results of doing this to a planet, they don't seem to deal with the consequences of such acceleration on everything on the planet.