"Well, do you mind if I look around the car a little bit?"

from Jay Z – 99 Problems Lyrics on Rap Genius

Meaning

Police may ask for your consent to search without a warrant. It’s considered voluntary even if you don’t know that you can refuse (which, of course, you can!)

See Schneckloth v. Bustamonte 412 U.S. 218 (1973)

A summons is issued in lieu of arrest. Therefore if a search is denied and the individual was in fact speeding, that individual may indeed be arrested instead of being given a speeding ticket. The car then is subject to a police inventory search in order to take inventory of all artifacts within the car before that car is impounded. If something turns up during the course of the inventory search it is allowed in court and is not a violation of the Exclusionary Rule set forth in Mapp v Ohio. Furthermore, if an arrest is to be made instead of issuing a summons a search of the individual’s person may be performed as the arresting officer is engaging in a search incident to a lawful arrest. Again, if anything is found on that person it may be used against them.

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