Zero. By the time you get to GEO your are connected to a station which is in Geostationary orbit. Your 35 hour ascent at say 1000km/h will have accelerated you sideways to the required 3km/second with a sidewards acceleration of 0.002g throughout the trip.
Of course you would be looking at a constant acceleration, not just a 1000km/hour trip. You'd probably be able to do the journey in a couple of hours with a reasonable acceleration and a rotating cabin (say 1.1g, meaning acceleration would slowly increase from about 0.1g at the surface, then after the flip point you'd decelerate at 1.1g). Even then sideways acceleration wouldn't be noticable (and your cabin could gimbal to just add it to vertical acceleration)
That's the other crazy thing. A space elevator takes forever at elevator, or car, or even plane speeds. But with constant acceleration/decelleration you can have a trip in airplane style seats with cabin crew serving you caviar // scratchcards (depending on class of cabin). Your peak vertical speed would be in the region of 8km/second - way above Earth's escape velocity, but you wouldn't even notice the acceleration/deceleration. You'd slow down in under 15 minutes.
Or you wouldn't and you'd depart Earth at 8km/s, twice the escape velocity.
(If you really wanted a fast departure you'd accelerate at say 1.2g and get upto 30km/s, twice the speed of New Horizons. 1.2g would probably mean you'd have the seatbelt on for the whole 40 minute trip)
You could launch cargo to Mars at say 5G, which would get it there in between 10 and 45 days depending where it is. Obviously you'd have a problem slowing down when you got there.