We all understand acceleration. It's the rate of change of velocity. This 4,891-pound Tesla Model S P100D does it best, reaching 30, 40, 50, and 60 mph from a standstill more quickly than any other production vehicle we've ever tested, full stop. In our testing, no production car has ever cracked 2.3 seconds from 0 to 60 mph. But Tesla has, in 2.275507139 seconds.

The Tesla does not hold the advantage forever, though, because higher speeds give the advantage to horsepower over instant torque. The Ferrari LaFerrari hits 70 mph a tenth of a second quicker; the Porsche 918 and McLaren P1 pull ahead at 80 mph, and these hypercars all continue to pull away at higher speeds. But around town, everybody has long since lifted off the accelerator pedal.

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Indeed all-wheel-drive cars capable of face-warping launches such as this latest, most ludicrous Tesla Model S P100D and November's wheelie-ing Porsche 911 Turbo S have us examining a lesser-known physics term: jerk. It's the rate of change of acceleration. Think of it as the difference between being accidentally pushed by a clumsy person and being aggressively shoved by a jerk.

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Launching a Model S P100D (weighing 5,062 with gear and driver) in full-on Ludicrous Easter-egg mode snaps your body in a manner that is utterly impossible to replicate in any other street-legal production car on normal tires and dry asphalt at a mid-$100,000 price point. We regard 0-30-mph acceleration times as the benchmark for how hard a car launches, and this new Tesla gets there 0.05 second ahead of the next quickest (aforementioned) 0.92-second 911 Turbo S. The two run pretty even through 40 mph, after which the Tesla pulls ahead, maintaining a 0.2-second lead from 60 mph through 90 mph. The two cross the quarter-mile mark together at 10.5 seconds, at which point the Tesla is running 125.0 mph, and the Porsche is traveling 6.8 mph faster.

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But let's back up and re-examine the launch. As you know, we start our acceleration clock the way the NHRA does: when the front tires cross the 1-foot mark. For the record, the Tesla hit that mark in 0.26 second, at which point it was already traveling at 5.9 mph for an average jerk rating of 121.5 ft/sec3. The Porsche did it in 0.20 second but was only going 5.4 mph. Yet it managed a jerk rating of 191.8 ft/sec3. The Ferrari LaFerrari bested them both at 0.19 second and 5.9 mph, jerking worth 233.6 ft/sec3—a remarkable holeshot for a rear-drive car.

But much of the jerk measured in that first foot is just driveline shock. Let's back out and consider the first full 0.5 second of acceleration, including that 1-foot rollout. Here we see the no-shock electric Tesla maintaining 76.2 ft/sec3 while the 911 Turbo S sustains 77.1 and the LaFerrari musters "just" 73.3—considerably better than the 52.5 and 53.1 ft/sec3 its hybrid hypercar rivals, the McLaren P1 and Porsche 918 manage. (To glean additional jerk-related pub ammo, see the attached chart showing these stats for all of our hardest-launching cars—including the predecessor P90D Ludicrous and, for perspective, America's most average car, the 2.5-liter Toyota Camry.)

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So how can you lay down a run like this in your very own P100D? First, find a safe closed course where the local constabulary won't write you up for reckless driving. Then ensure your car is running the latest firmware (v8.0 release 2.52.22), and select the Settings menu. Under Acceleration, press and hold the Ludicrous button for five seconds. As with the P90D, this prompts a warp screen of flashing lights followed by a screen that asks, "Are you sure you want to push the limits? This will cause accelerated wear of the motor, gearbox and battery." The two buttons below are marked, "No, I want my Mommy," and "Yes, bring it on!" Selecting the latter initiates a process of battery and motor conditioning, wherein the battery temperature is raised slightly and the motors are cooled using the air-conditioning system. It usually takes just a few minutes, longer in extreme ambient temperatures or after repeated runs. You should expect to wait a minimum of 10 minutes in between runs. The readout below the acceleration buttons will say ready when it's all set. Then you simply hold the brake, promptly tromp the accelerator, and quickly release it to initiate launch-control mode (which is verified on the instrument cluster display). Then firmly hold the brake for a split second while you nail the go pedal. Upon releasing the brake, you will rocket down the strip like Han and Chewbacca jumping to light speed.

The P100D's added verve also results in a slight improvement in its figure-eight performance, from the P90D's 24.7 seconds at 0.81 g average to 24.6 seconds at 0.82 g. That matches several other big-boned performers such as the Aston Martin Rapide, Dodge Charger Hellcat, Ford Shelby GT500, and BMW X5M. But none of those heavy hitters manages even half the jerk this Tesla delivers in a straight line.

Tesla Model S P100D Ludicrous Porsche 911 Turbo S Lamborghini Aventador LP-750-4 SV Nissan GT-R Track Pack Audi R8 V10 Plus 0-30 mph (sec)* 0.87 0.92 0.99 1.00 1.01 Time to 1 foot (sec) 0.26 0.20 0.20 0.26 0.22 Speed at 1 foot (mph) 5.9 5.4 6.1 5.5 5.7 Avg Jerk, 1-foot (ft/s3) 121.5 191.8 216.6 118.7 171.4 Avg Jerk, 0.5 sec (ft/s3) 76.2 77.1 75.9 61.2 79.7 *Excludes 1-foot roll-out time.

Tesla Model S P90D Ludicrous Ferrari LaFerrari McLaren P1 Porsche 918 Spyder Toyota Camry XSE (2.5L, 6A) 0-30 mph (sec)* 1.01 1.09 1.21 1.23 2.99 Time to 1 foot (sec) 0.24 0.19 0.31 0.25 0.31 Speed at 1 foot (mph) 5.7 5.9 5.0 5.6 4.3 Avg Jerk, 1-foot (ft/s3) 142.9 233.6 74.6 134.9 66.3 Avg Jerk, 0.5 sec (ft/s3) 70.5 73.3 52.5 53.1 37.5 *Excludes 1-foot roll-out time.