Does an aircraft hover at a constant acceleration or varied acceleration?

I have a question that's bugging me. Googling it only made me more confused so I really hope someone can help me clear this.

If a plane is flying up and down; or hovering (Like the x-wing scene from star wars for example, when yoda uses the force) does that result in constant acceleration or varied acceleration?

If the final velocity is 0, because it comes back to the same position, (please correct me if i'm wrong) and the time it takes to go up and come back down is 10 seconds, that would make a constant acceleration of (0/10) which is 0?!

EDIT: I know it sounds like such a weird question but the reason I'm asking this is that I'm doing a project on teaching academic subjects using pop culture (hence the yoda reference) and want to make sure the stated acceleration is theoretically correct.

EDIT: I drafted an image to help illustrate my question, I hope it helps. • You need to plot the position versus time. Then take the derivative of curve to get the velocity versus time. Then take the derivative again to get the acceleration. – Brandon Enright Mar 14 '14 at 23:59

There's not enough information.

For a simple hovering motion (or more precisely, no motion at all), the velocity is constant, so one would calculate a zero acceleration for the entire time interval. This is a consequence of the definition for acceleration $a\equiv dv/dt,$ since in any infinitesimal time interval $dt$, $dv=0$.

For a more complicated up and down motion, determining whether the motion is described by a constant or non-constant acceleration completely depends on the details of the motion. For example, if the X-Wing moves up at constant speed then comes down at constant speed, you'd end up getting a non-constant acceleration near the turn-around point. But if in each equal time interval $dt$ the velocity changes by a constant amount $dv$, the acceleration would be constant.

The effects of inertial acceleration is best understood from the physics of Newtonian mechanics.

A good site to support your understanding of this physics:
http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

I recommend studying the trajectory calculator as it applies to your problem.

• Can you explain it for the OP? – Dave Coffman Mar 29 '15 at 21:12