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Alright, here's the issue in its generic form:

I have D, the distance that must be traveled.

I have A, the acceleration constant of the camera.

And I need to find T, the time it takes to cover the distance if the speed is accelerating at A/sec.

Then there's the tougher part. To make camera movement smooth, I need the camera to reverse its acceleration halfway to the target, and slow down to a smooth stop at the end of the distance to be covered. This might not really fit into the physics, and be more of a programming issue for me to handle. If so, no problem, I'm moreso concerned with the core problem at the top.

I'm certainly being picky, but any help is most graciously appreciated! Thanks! :)