You are right that gravity gets stronger when you are closer to a
massive object (like the Earth). But that isn't the reason why a
falling object continues to accelerate. If the strength of the
gravitational field were constant over the entire 10 kilometers, you
would still continue to speed up during the entire trip.
Speed is measured in units of meters/second. Acceleration is
measured in meters/second^2. Acceleration quantifies the rate of change
of velocity. Multiply acceleration by time (really it's an integral,
but if the acceleration's constant you can just multiply) and you get
the change in velocity. Each second you remain in airless free-fall you
change you velocity by about 9.8 meters/second.
The reason parachutists reach a maximum speed is because of the
drag force of the air rushing by. This drag force increases with the
speed the parachutist falls at, and so there is a speed at which the
force of drag is equal and opposite to the force of gravity. Take away
the air and the parachutist will continue to accelerate.
If a parachutist starts at rest and falls 10 km in a uniform
gravitational field (not quite, but it's not a bad approximation), he
will be moving at 443 meters/second when he hits the ground. The whole
trip would take about 45 seconds. Adding in the effect of the air will
slow him down quite a lot.
(republished on 07/12/06)