This is specifically for british culture, I guess. There are quite a lot of references to the idea in victorian stories (e.g the introductory scene in 'Around the world in eighty days' etc.).
Basically, was it ever actually common belief that exceeding a specific speed would be fatal, or is it just an urban myth?
I'm having an impossible time finding a source for this, but when the train was first invented/becoming common, especially in the UK, there were urban legends that the speed of the train (even being inside of it) was too fast for humans to tolerate and could cause seizures, make it impossible to breathe, and even permanently damage your eyes because they wouldn't be able to adjust to the fast motion, although this was kind of the anti-vaxxers of the day, and not most people dismissed them as being ridiculous.
Yes a popular english 'science' writer Dr Dionysius Lardner in the 1820s and 1830s wrote that humans would find it difficult to breath at speeds above 30mph. Furthermore he thought eyesight would be damaged by the eyes trying to focus on scenery as it passed too quickly.
I can't find a source, but I remember reading that there were people that used to believe that going a mile a minute (60mph or ~100kph) would cause death. Also I've heard that 88mph could lead you to a whole new time, but I think it's just a legend too