What is the Halacha of establishing one's home at the onset of Shabbos?

Question

If one cannot make it home, I heard there's a din that one sets his place where they are now upto 2000 amot. What's the source of this? What if I'm in the back of a car?

Answer 1

This is passim in mishnayos maseches Eruvin, indeed it's the fundamental idea in that maseches^[1]: that one has, on Shabas (or yom tov), 2000 amos to walk in around where he started Shabas. If he started in a city, he has the entire city plus 2000 amos. See details there.

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^{[1] Well, in the part of it that deals with eruve t'chumin.}

Answer 2

This sounds like you're referring to the Mishna in Eruvin 4:7

מִי שֶׁבָּא בַדֶּרֶךְ וְחָשְׁכָה לוֹ, וְהָיָה מַכִּיר אִילָן אוֹ גָדֵר, וְאָמַר, שְׁבִיתָתִי תַחְתָּיו, לֹא אָמַר כְּלוּם. שְׁבִיתָתִי בְעִקָּרוֹ, מְהַלֵּךְ מִמְּקוֹם רַגְלָיו וְעַד עִקָּרוֹ אַלְפַּיִם אַמָּה, וּמֵעִקָּרוֹ וְעַד בֵּיתוֹ אַלְפַּיִם אַמָּה. נִמְצָא מְהַלֵּךְ מִשֶּׁחֲשֵׁכָה אַרְבַּעַת אֲלָפִים אַמָּה:

One who was on a journey and it became dark, and he recognized a tree or a fence and said, “Let my Shabbat place be under it”, he has said nothing. If he said, “Let my Shabbat place be at its root”, he may walk from the place where he stands to its root a distance of two thousand cubits, and from its root to his house another two thousand cubits. Thus he can walk four thousand cubits after dusk.

Not sure what the car has to do with Eruvin - unless you're asking if 2,000 Amot is time or distance; in Eruvin it's distance. (as opposed to Tefilat HaDerech and Matza baking where maybe the "distances" refer to time, based on how long it takes to walk that distance.)