"So we specifically asked for linear time."
"Uh, yeah, I did it in log(n). That's better."
"It doesn't match what's on this paper they gave me. Thanks for your time. We'll be in touch."
You’re expecting the mechanical engineer to recall something they learned about kinematics, not derive it on the spot. It’s a test of knowledge, rather than cleverness. The equations of motion are also more central to physics and engineering.
A decent programmer should know that linked lists exist, their general properties, pros and cons, etc. However, cycle detection is not a particularly common operation, so not knowing Floyd’s algorithm tells you very little—-and their failure to do years of research in 45 minutes even less.
The tortoise and hare algorithm is not the foundational skill required to make software work the way an understanding of motion is for building structures. That's why it's often omitted from educational material yet these people are able to produce usable software after even something like a bootcamp (which I guarantee basically no bootcamps ever touched this algorithm).
I'm not sure I approve of asking even more well known algorithms like Djikstra's algorithm or A* in a job interview, unless the role was something that specifically required that area of knowledge like building pathfinders for video games or robots or something.
Also, it took around 13.8 billion years for Newton to do what he did.
If they actually aren't looking for people who just cram CTCI or leetcode, coming to this answer from first principles is demonstrably far more difficult than you'd expect achieved in an interview.
These sort of questions have an incredible recency bias, and have zero relevance to engineering competence.
Of course; how else do you do back-door age discrimination?
Apparently the correct answer is to use "Robert W. Floyd's tortoise and hare algorithm", which is trivial to explain and code.
The catch?
It took a decade of computer science research between the original statement of the problem and Floyd discovering the solution.
So... no worries, you have an hour, a marker, and a whiteboard. Your time starts: now.