Translating baseparts + cargo?

I have been trying to smoothly translate a Part with players on it.. and have failed each and every attempt so far.

alpha and omega are both endGoal CFrames that the part tablet is meant to reach. However, the rides are really buggy and unstable. Is there a smoother method or function that takes into account the players and objects on the part?

        ...
            if toggle then
                for i = 0, 1, .01 do
                    tablet.CFrame = tablet.CFrame:lerp(alpha, i)
                    print(tablet.CFrame)
                    wait(.1)
                end
            else
                for i = 0, 1, .01 do
                    tablet.CFrame = tablet.CFrame:lerp(omega, i)
                    print(tablet.CFrame)
                    wait(.1)
                end
            end
        ...

[EDIT] tablet essentially functions like an elevator..