The vehicle it's strapped into is called a Sinclair C5. The Sinclair was a mid-'80s electric tricycle sold in the UK. Kind of a recumbant Segway, it was intended to be a new form of cheap and accessible transportation for the masses. It never caught on, mainly because of some design flaws that exposed the drivers to the elements, to safety issues when mixing with traffic, to pitiful performance, and to constant ridicule.
The jet here is a JFS100-13A Gas Turbine that has been converted into a turbo jet. It's the same engine they use as a starter (JFS = jet fuel starter) for the larger main engines on aircraft such as the A7 Corsair attack plane. It's also the same engine they used in that jet kart. It provides enough thrust to push this little C5 past 100 mph, if you are so inclined and stupid. The JFS100 can spin to an ear-splitting 72,000 rpm and runs on whatever you have on hand: jet fuel, diesel or even kerosene. If you are in the UK and this sounds like your cup of tea, we have some good news for you. This jet-powered Sinclair C5 is for sale at the reasonable price of just £3,999.99. You can see the whole conversion and images of the final product at the jetpower website. There are even videos of the trike in action.
Thanks for the tip, Derek!
[Sources: AutoblogGreen, The Register, Jet Power]