3. (physics) A wire is made into a right-angled triangle with legs of length $l=1$ m. From vertices A and B, two bugs start crawling along the legs simultaneously with speeds $v_{A}=5$ cm/s and $v_{B}=2 v_{A}=10$ cm/s (see figure). What is the minimum time after the start of their movement when the distance between the bugs reaches a minimum?

![](https://cdn.mathpix.com/cropped/2024_05_06_25c5d6100f66704b4a85g-2.jpg?height=354&width=354&top_left_y=1770&top_left_x=1545)