What is complexity of adding char in front of the string like s = c + s?

Because when I tested on c++ with code, its like O(1), but i think (but not sure then i ask here) i ever submitted at codeforces with this method, in O(n) loop then its get TLE (so the complexity O(n^2)), then i changed that part with other O(1) part then got AC.

What is complexity of adding on string like s = s2 + s1 with s1 is small string with length < 10 and s2 is n-long string?
What is complexity of adding on string like s = s1 + s2 with s1 is small string with length < 10 and s2 is n-long string?

Thank you codeforces community