Cool car, bud. That’s what a trendy 20-something guy said to me outside a shop last week as he cast envious eyes over this car.

He was right. The RS Q3 might not have a catchy name but, boy, everything else is pretty impressive.

What Audi have done is take a pretty sensible SUV and made it quick. Very quick. Nought to 60mph in 5.5 seconds is impressive for any motor, but for an SUV it’s astonishing.

You have to commend Audi’s foresight for realising such a concept would succeed. Audi has always had a penchant for making quick cars but to make a sporty SUV go with almost insane power - well, that’s thinking outside the box.

True, there will be limited demand.

The list price (£43,000 compared to £23,000 for the standard Q3) will see to that, as will the costs of running a 155mph, 310PS beast.

But vehicles with supercar performance are no longer limited to hatches and saloons. These days the sort of drivers who can afford such stunning cars are likely to be people with families with sporty lifestyles who need space as well as pace.

The RS Q3 is the first ever RS Q model. It debuted at the last Geneva Show with deliveries beginning late last year.

It is the first ever Audi SUV to be handed over to the specialists at Audi high-performance subsidiary Quattro for the full, no-holds-barred RS transformation.

It creates, in effect, a new performance class and it marked a busy 2013 for Audi which also unleashed RS 6 Avant and RS 7 Sportback. The RS family has grown to eight members – more than ever.

At the heart of the RS Q3 is a 2.5 litre TFSI engine familiar from the TT RS and RS 3 Sportback, linked to a seven-speed ‘S tronic’ twin-clutch transmission. From 2,480 cc of engine, it returns performance unparalleled in this class.

For the first time, the five-cylinder engine is also complemented by a standard start-stop system which offers impressive fuel economy of up to 32.1mpg on a combined route.

A five-cylinder engine might sound unusual but Audi aficionados will remember the legendary five-cylinder Audi Quattros of the 1980s. This model, I’m assured, sounds very similar.

To prove it’s a proper SUV, it has a permanent four-wheel-drive system which will keep you on the move in the harshest conditions. Drivers can alter the flap control for the exhaust system and the accelerator characteristic via the Audi drive select system. It offers auto, comfort and dynamic modes, and in the latter throttle response is sharper and the sound even more intense.

The clever electronics provide swift distribution of torque between the front and rear axles for optimum power management in all weathers.

It works with the RS sports suspension which lowers the body by 25mm compared to the standard suspension, and which is tuned to deliver flat cornering without forsaking comfort.

A specially tailored electronic stabilisation control (ESC) also stands guard – it offers a sport mode which raises the limit at which it intervenes, and it can also be deactivated entirely.

So, it drives well, but how does it look? Well, the Q3 is a neat-looking SUV but it’s hardly sporty in run-of-the-mill form but Audi designers have been hard at work with the RS version.

It has special body detailing, including a high-gloss black honeycomb grille and RS bumpers, a distinctive diffuser and large sporty tailpipes.

A roof spoiler, roof rails in matt aluminium and special door sill plates and door trim strips also add emphasis. At 4,410mm in length, the top ranking Q3 is 25mm longer than the standard car.

For even more differentiation, RS Q3 customers can choose an exclusive body colour – Sepang Blue pearl effect – from the list of eight available.

More RS signals are found inside. The instrument cluster has grey gauges with white scales and red needles and a flat-bottomed sports steering wheel. Drivers can call up the boost pressure, oil temperature and a lap timer via the RS menu in the driver information system.

Complicated? Yes, but easy to get accustomed to.

The luggage area has a base capacity of 356 litres, which can be increased to 1,261 litres by folding down the split rear seat backs.

A practical reversible load liner is standard, and customers who have even bulkier loads to transport can specify a towing bracket.

Being an Audi, it has a stunning navigation system and a Bose stereo, while Audi Connect means you have Internet connections.

On the road, it is a Jekyll and Hyde car. It feels fine pootling around town and it’s easy to manoeuvre in tight spaces, thanks to a sophisticated camera system.

But on the open road, it picks up speed smoothly and with real surge and menace.

No wonder Audi is on a roll. In 2013 Audi achieved best ever sales of 1,575,500 cars, an 8.3 per cent improvement over 2012.

Sales in the UK increased by 14.9 per cent year-on-year to 142,020 cars, establishing another record and meaning Audi is the leader in the premium sector for the first time.

Audi RS Q3 PRICE: £43,000. The standard Q3 costs from £23,879 ENGINE: a 2,480cc, five-cylinder unit generating 310ps via a seven-speed automatic gearbox PERFORMANCE: Top speed COSTS: Combined 32.1mpg EMISSIONS: 206g/km WARRANTY: Three years, 60,000 miles