If you’ve ever been to Alton Towers, you’ll probably have heard of Rita.

Originally dubbed ‘The Queen of Speed’, Rita is a 640-metre long accelerator coaster that propels her passengers from rest to just over 60mph in 2.5 seconds, during which their screaming bodies are subjected to over 1.1g.

It perhaps wasn’t the best choice of ride for me to lose my roller-coaster cherry to, but nearly 10 years ago, I found myself being strapped in to a car along with 40 excitable kids, who all apparently knew what was to follow.

I didn’t.

What I learned – in about two point five seconds – was that if you don’t put your head back against the seat, you get to spend the next three days walking around with neck pain.

This week, I had a strangely familiar experience.

Sat behind the wheel of Tesla’s new Model S P85D, and with the acceleration set to ‘Insane’ (no, it really says that), I mashed the accelerator pedal into the carpet and held on. I even remembered to put my head back.

Tesla’s figures claim a 0-60mph time of 3.1 seconds, and I’ve driven cars with that level of performance before. So this time, I thought I knew what to expect.

I still didn’t.

Nothing prepares you for the acceleration that can be achieved by a power-plant that’s capable of deploying maximum torque (all 931Nm of it) at zero rpm.

Try the same trick on a rain-soaked road in a P85+, the previous Model S flagship, and the chances are you’ll fishtail your way into a hedge; all the traction control in the world can’t reign in that kind of force when it’s sent to just two wheels.

But in the new P85D, which I drove on UK roads for the first time ahead of its arrival in Tesla stores later this year, the sensation is just like the one Rita gives you. A rail-guided slingshot to the horizon.

A rail-guided slingshot to the horizon.

That’s because the ‘D’ stands for dual-motor: in addition to the 470hp rear motor, there’s a second 221hp motor mounted on the front axle.

Of course, that gives the Model S all-wheel-drive, and that means it’s not only more powerful, with a combined output of 691hp, but also much easier to get off the line. There’s no launch control; no part-time park employee to strap you in: you just put it in Drive and put your foot down.

Unlike conventional cars, there’s no need for a heavy transfer case or complicated driveshaft layouts.

In fact, Tesla found the dual-motor platform to actually be more efficient despite the weight penalty of the extra motor, with dual-motor models gaining an extra 10 miles of battery range over their single-motor compatriots.

If you have friends over for the weekend, you might find yourself putting a serious dent in that range, however, as they repeatedly insist you demonstrate your own personal roller-coaster.

Part of what makes the experience so addictive is the serenity in which it happens. Blast to the legal limit in a McLaren, and there’s an assault on the senses that goes with it: the sound of turbos spooling up, eight cylinders consuming the atmosphere, and the visceral jolt of at least one gear-change.

In the Tesla, there’s none of that. You’re loosely aware of a muted whine as the motors spin like turbines, the numbers on the speedo scramble to keep up, and your innards climb into the dark recesses of your backbone as if looking for safety.

It’ll hold its line through the bends better, too, the car adjusting the balance of power distribution front to rear 100 times every second. You’re still aware that this is a big, heavy car – over 2.2 tonnes, in fact – although with the weight down low there’s less of a pendulum effect and more just the sensation of weightiness.

As noted in our Model S review, tyre noise is still an issue, the ride quality isn’t the best, it’s too wide for UK roads (it won’t fit through most width restrictions in London), and you could argue it ain’t cheap.

A P85D will set you back £80,280 after a £5,000 Government grant (and you’ll need to be quick to claim it, as the scheme is set to end soon), although the less powerful but still dual-motor 70D can be yours for £55,380.

But then what do you compare it to? Similar performance from Porsche will cost you £120,000 and the ability to carry more than one passenger.

A £200,000 McLaren? An £8million theme park ride?

There truly is nothing else quite like it on the planet.

Entry-level Price£80,280Price as tested£97,000 (est)
EngineElectric motorsTransmissionNone
Power470hp + 221hpTorque931Nm
0-603.1 secsTop speed155 mph
EconomyCO20 g/km
Dimensions4970 x 2187 x 1435 (LWH)Kerb Weight2239 kg