I've made a small edit to this puzzle to try to make it slightly more difficult; see the edit history for the original version.

The other day, I was taking a driving lesson. My instructor was sitting directly behind me, as usual, while I was driving steadily at about 60 miles per hour.

The instructor told me, "Slow down to 40 miles per hour, and maintain that speed." So I slowed to 40 miles per hour, as she asked, but I found that it was impossible to maintain such a slow speed; I felt a horrible lurching sensation as the vehicle started accelerating again. The instructor said, "You just learned why it's important to keep your speed up!"

Next, the instructor asked, "If we wanted to stop the vehicle right here and now, would that be possible?" As a joke, I replied, "Only if we ran out of fuel!" She laughed.

The instructor then said that actually, we would be able to stop right there and then if we wanted, and she explained how. Of course, if we were to stop using that technique, we wouldn't be stopped for very long.

Anyway, I continued driving along at about 60 miles per hour until the trip reached its natural ending point, and the vehicle stopped. At this point, the vehicle was obviously unusable, so we had it towed back to the garage.

What kind of vehicle was I driving?

Oh, by the way, if it helps, the trip began and ended at a weather station.

• ""Only if the engine broke down!" She laughed, since that was obviously impossible." There seems to be an obvious answer from this line alone. Jan 26, 2020 at 8:12
• @Randal'Thor Maybe that part made things a little too obvious? :) I decided to try removing that part—though I'm not sure if I made things better or worse. (My edit turned your comment into a spoiler, for what it's worth.) Jan 26, 2020 at 18:26
• I like this version better Jan 26, 2020 at 21:54

Were you driving a

glider?

(Explanations follow, but I'm not a pilot, so some of them may be way off.)

The instructor was in the back seat, because

gliders are sleek, and there wouldn't be room for two persons side-by-side.

You can't go slower than 60 mph, because

the glider will stall, explaining the lurching sensation.

The engine won't break, since

you don't have one.

You can probably stop by

picking up some extra speed (by diving down), and then bringing the nose up as much as it goes, so that the glider climbs until its speed runs completely out. This would cause a another stall (not stopped for long), but this kind of stall is very hard to recover from, which is why this was only an explanation, and not a demonstration.

Once the journey stops,

a glider on the ground

will be quite unusable, and is usually towed to storage.

• The question now refers to running out of fuel, I suspect it might be a similar vehicle but with an engine Jan 26, 2020 at 22:05
• @MooingDuck The new version has the same intended answer. Jan 26, 2020 at 22:26

You might have been in

a glider (or sailplane).

In such a vehicle,

✔ training is done in a two person model, and the instructor sits behind
✔ stall speed is often around 40mph, so trying to keep that speed would be tricky, and a shallow stall would cause it to dive - picking up speed with an unpleasant sinking sensation
✔ there is, of course, neither an engine to break (original version of the puzzle) nor fuel to run out of
✔ there's actually a few ways to "stop" -- it's possible to ride a thermal or be met by opposing wind such that you briefly glide in place without net movement; you can also either air-brake, or climb straight up, either of which will stop your forward motion and, in the case of the climb, eventually use up all your momentum leaving you motionless at the top of your climb, though these latter options induce a stall you can't do this for long before you're falling
✔ at the end of your flight, your glider cannot self-launch, so needs to be towed back
✔? launch can be done in different ways; some are launched by means of a winch, but often they are towed and released by other aircraft. @Alain Remillard points out in a comment that most airports have their own weather station, so a glider might well be taking off and returning home at an airport/weather station.

• I think your missing piece is rot13(Hfhnyl Gurer vf n jrngure fgngvba ng rirel nvecbeg.) Jan 26, 2020 at 11:42
• @AlainRemillard Good thought; added :)
– Rubio
Jan 26, 2020 at 12:52
• I think I need to start adding check marks to my answers.
– Bass
Jan 26, 2020 at 13:42
• Nice answer! Sbe fgbccvat va zvq nve, gur znarhire v unq va zvaq jnf jung jvxvcrqvn pnyyf n gnvyfyvqr. Chyy hc fb gung lbh'er sylvat fgenvtug hc; tenivgl jvyy fgbc lbh, naq gura fgneg lbh ntnva va gur bccbfvgr qverpgvba. Jan 26, 2020 at 14:33
• @Bass I've re-read both answers, and I've decided that your answer is a bit more accurate after all. Of course, both answers are nearly perfect and it's hard to choose between them. In any case, the reason I commented on this answer is that I disagreed with part of it, and the reason I didn't comment on yours is that I didn't disagree with any part of it. Jan 26, 2020 at 16:10