Liz McIntosh had been driving the vehicle along a road on her 700-acre sheep and cattle farm at West Todholes, Elsdon, in North West Northumberland.
She was seen by her postman get ting off the quad bike, which was towing a trailer, to open a gate.
The inquest heard that the vehicle was still in gear, with its engine on and hand brake off, and most likely started to roll.
It was thought the 64-year-old tried to then control the quad but was unable to and it carried on moving.
The vehicle then hit the verge and the trailer tipped, crushing Ms McIntosh beneath it, the inquest at Berwick Magistrates’ Court was told.
She was discovered moments later by her neighbour but had already died.
A post-mortem examination revealed the cause of death was traumatic asphyxia, meaning she was unable to breath after her chest was crushed.
PC Darren Sanderson, part of Northumbria Police’s Collision Investigation Unit, told the court tyre marks at the scene and the fact the quad had veered to the right, indicated Ms McIntosh had tried to stop the vehicle rolling. He said: “The vehicle was on a downhill gradient, was left in gear and without the hand brake on. The vibrations from the engine may well have caused stones and gravel beneath, which may have acted as a stop, to move and the vehicle begin to roll.”
A friend told the inquest Ms McIntosh lived life at full throttle and always had “101 things to do”.
Recording a verdict of accidental death, north Northumberland coroner Tony Brown said: “Elizabeth Anne McIntosh had lived at West Todholes Farm for 30 years.
“She was described by her employee Mr Tully as an experienced farmer.
“On Friday, January 11 2013, Mr Tully spoke to Elizabeth and said she was her normal self. Elizabeth was seen walking from her quad bike to open a gate on the track between West Todholes Farm and East Todholes Farm between 2.15pm and 2.30pm by her postman.
“At 2.30pm her neighbour was returning home and found Elizabeth beneath her trailer, which was attached to the quad bike.
“Paramedics were called but nothing could be done for her and her death was pronounced at 15.04pm.
“Police inquiries showed the quad bike was only four months old and had no mechanical defects.
“The trailer, although old, was in a good condition.
“It was likely the vehicle was parked on the side of the road, on a slight gradient. It may well have started to roll forward without the hand brake being engaged.
“Elizabeth may well have tried to regain control of the vehicle before it overturned and caused her death.”
Divorced Ms McIntosh, a well-known and well-loved farmer, was born in Newcastle in 1948.
She was a chartered forester who set up her own company, Forest Design Services. Among other projects, in 2008 she was commissioned by Scottish Woodland to evaluate the tree planting plan for Threestone Forest on the eastern edge of the Cheviot Hills.
She also allowed young fieldwork and ecology students to use her farm for course studies.