the below notes contain the specs needed.
my answers are as follows.
1) what would be the escape velocity/speed of a vehicle
that is leaving earth and traveling into outer space?
A1: any vertical velocity / speed above zero.
2) how much force would the vehicle first need to accelerate
itself vertically off of the ground?
A2: a force greater than 1 kilogram force.
3) how much extra force above the required lift off
force would the vehicle need to acquire a vertical
acceleration of 1 meter per second per second?
A3: None.
4) as the vehicle achieves vertical acceleration and as the vehicle gets further away from the earth and thus further away from the pull of the earths gravity wouldn't the vehicles vertical velocity and vertical acceleration increase due to the increased distance from the center of the earths mass if
the vehicle is propelling itself with the same amount of
force that it used for lift off?
A4: Yes.
notes:
a) the mass of the vehicle is 1 kilogram.
b) there is no fuel , the vehicle can provide a
constant force for propulsion and so propels itself.
c) the vehicle has stabilization equipment to keep the
vehicle in a vertical posture.
d) and of course taking into consideration that
building such a vehicle is possible.
e) the vehicle can only lift off the ground and travel vertically not horizontally.
f) and assuming there is no air or downward wind resistance.
https://en.wikipedia.org/wiki/Escape_velocity
