The aircraft would have to be at a heck of an altitude, and almost stable in its fall, to take three minutes.
Let's say the aircraft was a fighter, the size of a Bf109, and at 10,000 feet when it began it's descent, in a dive at around 45 degrees angle, not spinning or falling end over end, and structurally intact.
Time to impact would then be anywhere between around 20 to 60 seconds, possibly faster, depending on the speed of the aircraft.
A human body, in freefall in a stable, spread position, falls at 200 feet per second, eventually reaching a terminal velocity of 120 mph ( the first 11 to 12 seconds are in acceleration ). If the parachute is not deployed, impact will happen after 50 to 60 seconds, depending on air density, wind etc.
An aircraft, being heavier, and already travelling at probably 150 to 300 mph, is going to descend a lot faster.
As mentioned, it is not possible to give a 'blanket' figure for the time taken, or speed of descent / impact for an aircraft, as it depends on the type, weight, speed, altitude, descent angle etc etc.
Edited to correct typos etc.