The certified flight instructor (CFI) stated the airplane hit a bump on the takeoff roll, and became airborne prematurely. The airplane veered to the right at a very slow airspeed. At that point, the CFI elected to continue the takeoff, rather than land. He lowered the nose to gain airspeed; however, he was unable to attain sufficient airspeed and altitude to clear trees that were ahead. The airplane collided with the trees, then impacted the terrain.