Trevor Hudson's Legacy - S5-E18
Revealing mistake: There are 2 scenes involving Jessica inside a car. In the first one the car drives calmly as seen from the outside shots, but from the shots inside the car is speeding. When the episode is about to end the car speeds to the police station and now the exact same projection is played, though this time it makes sense.
Answer: In a flashback scene, it was shown that he had a violent temper, so it stands to reason that he finally killed her in a fit of rage.