The cars would travel at up to 200kph and arrive at the space station eight days after departure from Earth. These early cable experiments are important, but someone should also be working on the composing an 8 day Elevator Muzak score that won't drive you insane.
Weird to me that they aren't accelerating till the midpoint and then breaking till the destination at a constant 1g. Gets around the space sickness by providing artificial gravity and should take ~hours rather than ~days.
So, there's surely a safe speed limit built into the materials being used? It's probably faster than the speed they're starting out with, but I kinda assume it can't be fast enough to shorten the trip to hours from days.
As an aside, moving people is probably not the most profitable use of the thing for the foreseeable future, as cool as that sounds. Getting a satellite into orbit for a tenth the cost is revolutionary (though they mention the cost compared to the shuttle, which is much more expensive than rocket transport...so they may be cherry-picking numbers to make this seem more revolutionary than it is).
Anyway, I can't think of how they could accelerate much beyond the fastest non-maglev train speeds without tearing apart the cable and car, but I may be underestimating the strength of carbon nanotubes, and whatever other component materials they're using. Perhaps there's a materials nerd here who knows.