Project: FATE is a free first person adventure/puzzle/exploration game inspired by the likes of Portal and Myst. The game is centered around a combination of exploration and physics-based manipulation, using robotic 'pawns' with unique properties that allow movement and interactivity.
The doors with the stopwatches on them are timed gates. When the player steps on the button connected to them, a timer starts, and the door closes when the timer is over.
This is room one of a larger puzzle that involves every mechanic learned in the game in the airport area. (area 1)