Accelerating from zero to 60 in the 707-horsepower Jeep Grand Cherokee Trackhawk is the automotive equivalent of a ride in the Orgasmatron employed in the early Woody Allen comedy Sleeper.

To evoke that sensation from this high-performance luxury SUV: Put the driving mode selector on "Track,"  press hard on the brake pedal with your left foot, hit the "Launch" button on the console, let the electronics do their Merlin act on the supercharger and the rest of the intake system, then nail the gas and release the brakes.

The result is something akin to a space vehicle bursting free from the fiery bowels of a missile silo. An unseen wall of power shoves you back in that lovely leather seat. A wall of sound accompanies the blast-off. Zero to 60 is accomplished in about 3.5 seconds. (That's Jeep's number; a Motor Trend writer reported doing it in 3.4.)

Is that quick? Do bears picnic in the woods? That number makes the Trackhawk the quickest production SUV on the planet — for the moment, at least. Indeed, it would take an exotic sports car costing three or four times as much to rival or exceed that sort of stoplight skedaddle—and they wouldn't be dragging around over 2.5 tons and providing expansive cargo space, off-road prowess, and the ability to tow 7,200 pounds.

Power for the Trackhawk is courtesy of a supercharged, 6.2-liter Hemi V-8 that distributes trailersful of horses and torque to all four wheels via a beefy, eight-speed automatic. This is the engine that debuted in the Dodge Challenger Hellcat. The engineers say the Hellcat-equipped Grand Cherokee does a bit better launching job than the rear-drive Challenger Hellcat by virtue of its 4WD system.

In addition to beefing up the engine to deal with the additional power engendered by the supercharger, myriad changes were made to the Grand Cherokee's suspension, brakes and front-end design to keep pace with the higher engine performance.

The standard brakes were replaced by huge Brembo high-performance binders, sporting six calipers per wheel up front and four aft. (I've encountered precious few sporting machines with that many brake disc squeezers.) The result is a system that brings the portly, 5,300-pound Trackhawk from 60 to rest in a mere 114 feet.

The Trackhawk is also an inch lower than a standard Grand Cherokee and employs a Bilstein adaptive damping system that keeps things flat and poised in the corners when in the firm "Track" mode — and more comfy in the "Auto" setting.

The Trackhawk's body is fitted with a number of unique design elements. Some of them are practical, like substituting cold air intakes for the fog lamps to increase the supercharger's oxygen ration. Others, like the four-outlet exhaust, supercharger badging, and front-end styling changes, are cosmetic.

The interior of the 2018 Jeep Grand Cherokee Trackhawk offers unexpected comfort.
The interior of the 2018 Jeep Grand Cherokee Trackhawk offers unexpected comfort.

The handsome Trackhawk body cohabits with an interior as gorgeous as it is rich. The tester had a dark red and black cabin that featured lovely, supple leather seats and eye-capturing carbon fiber accents.

One of the interesting things about driving the Trackhawk is the unexpected comfort and civility afforded by a vehicle with so much raw power and athleticism. In "Auto" mode, it is quite comfortable and even docile in urban settings.

Predictably, given its power and weight, the Trackhawk doesn't consume fuel with baby's first spoon. It has EPA mileage ratings of 11 city and 17 highway, which aren't going to earn it an honorary degree from the Sierra Club.

And with a base price of $85,900, it has certainly exceeded this baggy-pants newspaperman's ability to pay.

2018 Jeep Grand Cherokee Trackhawk
Base price: $85,900
As tested: $101,555
Standard equipment: 6.2-liter engine, eight-speed automatic transmission, on-demand four-wheel-drive, and a feature litany that includes an extensive array of electronic safety devices, high-performance brakes and suspension, heated and ventilated front seats, a heated steering wheel with power tilt/telescopic feature, and headlight washers
Options: Include a $1,995 rear-seat, dual-screen Blue Ray and DVD player, a $4,995 leather package, a $1,995 19-speaker sound system, and a $2,095 sunroof
Fuel economy: 11 city and 17 highway
Engine performance: Wow to the third power
Handling: Adroit
Styling: A real studmuffin
Ride comfort: Surprisingly good
Warranty: Three years/36,000 miles bumper to bumper
Four bens: Excellent