A wire of length $4$ is bent into a square. At time $t = 0$, a bug starts crawling from the corner of the square to an adjacent corner, and continues traveling along the rest of the square until it reaches its original starting point at $t = 1$ (the bug's speed is constant). Given that the center of the square is $O$, the bug's starting point is $A$, and the bug's location at time $t$ is $B$, how much is the measure of $\angle AOB$ changing at time $t=0.3$? Angle measures are in radians.
2026-03-29 19:08:22.1774811302
A Bug Crawls Along a Square
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Use a bit physics. $\dfrac{d\theta}{dt}=\omega=\dfrac{v_\perp}{r}$.
Take component of speed perpendicular to $OB$ and $r=OB$