The pilot of a power-glider reported that, while on final, he observed that his ground speed was higher than his indicated airspeed. Upon landing on the first ¼ of the 2700 ft runway, the powered-glider veered left and he corrected with left brake and rudder, and the power-glider overran the runway, and impacted a tree. The powered-glider sustained substantial damage to the fuselage and the left wing. The pilot reported that there were no preaccident mechanical failures or malfunctions with the powered-glider that would have precluded normal operation. The automated weather observation station located 6 NM east of the accident reported that, about the time of the accident, the wind was variable at 5 knots. The powered-glider was landing on runway 26. The pilot further reported that he was later told he touched down beyond halfway down the runway and the pilot recommended not landing with a tailwind.