The pilot received an airways clearance to track to Adelaide via Quarry. He was issued with air traffic control instructions to descend to 3,000 ft above sea mean level (AMSL) for an instrument landing system approach and to maintain 320 kt until 28 km from Adelaide. The pilot queried this requirement due to difficulty in scheduling the flaps and landing gear speeds in the distance remaining from the 28 km position to the landing. A more acceptable requirement to maintain 320 kt to 36 km was obtained. At 33 km from Adelaide, while passing through 3,400 ft AMSL in cloud, with a sink rate of 1,300 ft/min and an airspeed of 310 kt, a ground proximity warning system (GPWS) mode 2 activation occurred. The pilot immediately followed company requirements by initiating a climb to 4,500 ft, being the lowest safe altitude for the area, and advised ATC accordingly. An uneventful instument approach and landing was then carried out. The Adelaide Approach Controller advised that the aircraft had been maintaining ground separation in accordance with the radar terrain clearance standards prior to commencing the climb. A combination of a fast speed and high rate of descent in the vicinity of steep hills is a known cause for GPWS activation.