What is the fastest accelerating aircraft on takeoff?
Airplane performance really isn't gauged that way, partly because quick acceleration 'drag race' data is not a pertinent aspect of their flight envelope.  That being said, there are a few examples, one being from the TV show Top Gear where a Bugatti Veyron races a Eurofighter Typhoon - and gets smoked by the jet.


                
            

I don't have data on jet fighters as far as linear acceleration; a quick calculation could reveal some basic data.

Take the case of an F-22.  Assuming a 55,000 lbf takeoff weight, lineup, 70,000lbf thrust at full power, then brakes off and rolling, we expect to see an acceleration around:

$$(70/55)*32.2 ft/s^2 = 41 ft/s^2$$

This also assumes no friction from the wheels or air resistance during the takeoff roll.

By basic kinematics, the jet would reach 60mph or 88ft/sec in 88/41 = 2.15 seconds.

So could an F-22 or another high performance jet fighter beat an Model S in a drag race?  Well it's theoretically possible and and as the above example shows, it has happened and it didn't end well for the auto.

As for airliners, the car is going to smoke them until the car reaches Vr for the jet or thereabouts.

And there is no way in hell a Model S is going to do 0-1000 mph.