Bruce Jenner -- Speed at Impact in Fatal Crash ... 38 MPH

Bruce Jenner was traveling at 38 miles an hour when he struck the Lexus on Pacific Coast Highway earlier this month ... according to data retrieved from his SUV.

Law enforcement sources tell TMZ, the Sensing Diagnostic Module (data recorder) shows Bruce was traveling between 46 and 47 MPH when he slammed on his brakes. Our sources say impact occurred almost immediately after braking.

That would mean Bruce must not have seen the cars backed up at the light until the very last second, which could explain why he was casually holding a cigarette as the cars collided.

TMZ broke the story ... an MTA bus captured the entire crash, showing Bruce's SUV hitting the Lexus, which went into oncoming traffic and struck a Hummer, killing the Lexus driver. Bruce then hit the Prius that was in front of the Lexus.