A driving system for a vehicle includes drive source, a driven portion, a unidirectional power transmitting unit provided on a power transmission path between the drive source and the driven portion, and having a first member, a second member, and an engaging element interposed between the first member and the second member, and an eccentricity acquiring unit adapted to acquire an eccentricity, the eccentricity being a magnitude of deviation between the rotational axis of the first member and the rotational axis of the second member.