Is this the right wording. search is a sentence that can stand on its onw?

No, "search" is not a complete sentence. It's a noun, and nouns don't form complete sentences on their own.

To make a complete sentence, you need a subject and a verb. Here are some examples:

* The search was successful. (subject: search; verb: was)

* We conducted a thorough search. (subject: we; verb: conducted)

* I am searching for my keys. (subject: I; verb: am searching)