Just over two weeks since his dramatic acquittal for the murder of Trayvon Martin, 17, Zimmerman was issued the warning on Sunday in Forney, Texas, just 25 miles from Dallas.
The latest traffic incident comes a week-and-a-half after Zimmerman rescued a family-of-four from their upturned SUV over a thousand miles away in Florida, near where he shot Martin dead.
With Zimmerman facing death threats following his acquittal, his brother Robert said that his family have to deal with rumors about his whereabouts every day.
He added that they go to great lengths to ensure their safety in accordance with the law.
CBS Dallas Fort Worth have claimed that the officer did not recognize Zimmerman, who has been at the center of a nationwide controversy since he was found not guilty of the second-degree murder and manslaughter of Trayvon Martin earlier this month.
Indeed, Zimmerman is even reported to have asked the officer if he knew his face from television and the officer again told the one-time Florida neighborhood watch captain that he did not.
While being questioned by the officer, Zimmerman, who was driving a 2008 Honda pick-up with Florida plates, told the officer that he was armed and was instructed to keep the gun in the car's glove-compartment.
The officer issued Zimmerman a warning for speeding and then sent him on his way - but not before asking him where he was going, to which he replied 'nowhere in particular'.
'Nowhere in particular, why is that?' responded the officer according to In Forney.com
'You didnít see my name?' said Zimmerman. The officer then responded,'wow, what a coincidence.'
The officer then inquired if Zimmerman was free of any warrants for arrest, to which Zimmerman replied,'absolutely'.
'Alright, Iím gonna go back and just check you, routinely,' said the officer as he checked Zimmerman's proof of insurance and a driverís license.
'The reason you were stopped was for your speed, why donít you slow down a little bit for me and, as long as you donít have any warrants, Iíll cut you loose with a warning,' said the officer to Zimmerman according to In Forney.com .
'Just take it easy, go ahead and shut your glove compartment and donít play with your firearm, ok?'
The traffic stop according to InForney.Com lasted approximately five minutes and after being given a warning, Zimmerman was sent on his way - being wished 'a safe trip' by the officer.
In the aftermath of his acquittal Zimmerman's lawyers said that he would almost certainly rearm himself and would be handed back the 9mm Kel-Tec pistol he used to kill Martin.
Federal investigators have not yet returned the weapon.
And even though the fact that Zimmerman is back carrying a weapon will certainly be viewed as controversial, Zimmerman is legally permitted to under Texas state law.
The gun in the glove box is legal in Texas, and police routinely ask motorists if they have weapons in the car, Brooks said. He said the entire stop lasted less than five minutes.
'It wasn't for super-excessive speeds, they just got him on regular speeding,' said Brian Brooks, city manager of Forney, Texas, about 25 miles southeast of Dallas, where Zimmerman was stopped.
'It's a pretty routine stop except for the fact that it was George Zimmerman.'
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