Ah yes! I've only felt that 'push in the back' when power is increased in the air in 2 aeroplanes - Concorde and the Yak 52!
And yes again - one of the things that amazed me when checking out in the '52 was the prodigious descent rate with power off, fine pitch, flaps and gear down. When Martin first demonstrated it at the downwind / base turn (level with the numbers!) I didn't think we'd land in the same county, never mind on that runway down there between the wing root and the cockpit side.
But demanding though the '52 can be, especially if you screw up aerobatic manouvres (it has a propensity to spin in interesting ways), it's a pussycat to land. In fact as long as the pilot holds the nosewheel off for as long as possible the beast lands itself!