Whomobile

The Whomobile was a futuristic-looking vehicle designed by the Doctor, which was similar to a hovercraft and also capable of flight.

The Doctor first used the vehicle to search for the secret base of Operation Golden Age. (DW: Invasion of the Dinosaurs) It was later used to chase after Lupton when he stole the Doctor's Metebelis Crystal. (DW: Planet of the Spiders)

The name
The vehicle was not created for Doctor Who, but was personally commissioned by Jon Pertwee, who retained possession of it after his stint as the Doctor. Pertwee gave it the name "Whomobile" during press interviews, but it was also known — again, offscreen — as "Alien". Had the vehicle been named in Doctor Who, it almost certainly would not have been called "the Whomobile", as this violated producer Barry Letts' strong conviction against making plays on the programme's title. The Doctor Who Technical Manual referred to it simply as "The Doctor's Car."

However, the name was uttered in an audio drama featuring Pertwee and Elisabeth Sladen recorded for Glorious Goodwood, but which was never released until it appeared one of the Doctor Who at the BBC CDs in the mid-2000s.

As a real-life vehicle
The Whomobile was one of Jon Pertwee's personal vehicles. He retained possession of it until nearly the end of his life.

When Pertwee demonstrated the vehicle on an episode of Blue Peter during his tenure, he revealed that the vehicle was road worthy and legal, though he mentioned that the BBC forbade him or any of the crew from removing it from the studios except for outside shoots. It was capable of a top speed of 105 mph.

As documentary subject
Pertwee presented the Whomobile in the documentary Thirty Years in the TARDIS.