How far does a cop have to pull you over before its illegal after a volation?

In the United States, there isn't a specific distance that dictates when a police officer's stop becomes illegal after a violation. Generally, the officer must have reasonable suspicion or probable cause to initiate a stop, and this can occur at any point after a violation is observed. However, if the officer takes an excessively long time to initiate the stop after the violation, it may be subject to legal challenge based on the circumstances of the case. Ultimately, the legality of the stop depends on the specific facts and context surrounding the situation.