That's a good point, thanks. I ended up having a look through the differences between detention and arrest (finding different thresholds, e.g. "reasonable suspicion" vs "probable cause"[1], and that "20 minutes or so is a reasonable timeframe for detaining someone" [2]).
[1] http://www.nolo.com/legal-encyclopedia/arrest-vs-detention-h... [2] http://criminal-law.freeadvice.com/criminal-law/arrests_and_...