Mr Goodwin told the committee he was seeking answers from the trust to "bring clarity to an issue which has been bubbling on for some time".
He was supported by councillor Gary Caffell who said he had asked questions of the trust over quite a long period and had not received replies that satisfied him.
He said the trust had an important role to play in making the athletics track work.
"It is not working now as it should be," he said.
Mr Caffell said the trust did not appear to have enough money to be able to deal with unplanned costs "if something major happened" and "somewhere along the line the council may have to seriously look at taking over that side of things".
Councillor Chris Peterson voted against putting the questions to the trust for answer along with Pip Hannon and Graham McClymont.