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TMZ Sports has obtained a video shot seconds after a photographer collided with Ohio State quarterback J.T. Barrett on Saturday ... and you can see Barrett limping away in pain.

The person who shot the video had great seats for the OSU vs. Michigan game and had been recording Barrett as he warmed up in the early minutes of the game.

The witness says he didn't record the collision -- but managed to capture the direct aftermath ... and you can see Barrett limping.

The witness also says the perpetrator had already run away from the collision site by the time he got his phone back up and running ... but ID'd the photog as a white guy in gray and yellow gear who was carrying a "medium-sized camera."

OSU coach Urban Meyer initially called for an "all out investigation" into finding the photog -- but later walked that back and said the program is just trying to find out what happened, so the NCAA can help make better sideline procedures.