How to know if a vehicle is moving without any external source of information?
You cannot tell moving with constant speed apart from standing still. This is the principle of Galilean relativity.
As an abstract spherical-chickens-in-a-vacuum-type question, then no, basic relativity says not.
But that isn't much fun. ..
First up, what do you mean by speed? If you mean speed along surface of earth then you have a chance. Since the earth is curved you are always accelerating, and you could measure the drop in g as you speed up. So long as you don't go fast enough to go into orbit... Of course the is some degeneracy between speed and altitude for this.
Of course. If we are moving on a true straight line it is easier still as you will move through the earth's gravity as you pull away from the surface. Or burrow beneath it!
A more practical method (that is actually used) would be dead reckoning. If we assume (or assert!) that the vehicle was stationary when you got in then you can in principle detect every acceleration the vehicle makes from then on. Integrating these will give you your current velocity. Of course the accuracy of this method decreases with time as the errors simply accumulate.
Finally, if our vehicle is ground based, then an oddity of fiction could at least tell us if we are probably moving or stationary. Friction between surfaces is typically very different for static and dynamic friction, with static being stronger. This means that when something slides to a stop (be it a sled or break discs) it almost always jolts slightly at then end as the stronger static fiction kicks in. You will feel this on buses and trains frequently. Although careful control can minimise the jolt, looking out for it with a sensitive accelerometer would give you a strong hint you had stopped.
Actually special relativity states that all inertial reference frames are equivalent, so there is no such thing as absolute speed.
You can't ask "What is my speed", this question is just not well formed. You can ask: "What is my speed in reference to this object", and in fact all "real life" examples of asking "What is my speed" actually have some implied reference frame. Traffic sign specifying that maximal speed is 50 km/h, reall specifies that: "Maximal speed of car in reference to road surface is 50 km/h".
In case of moving on earth you allways have a handy reference frame (that is: earth) and you can measure:
- Your speed in reference to air.
- How fast wheels of your car are moving.
- You could measure speed using GPS
Without Earth as reference frame (or some othere reference frame) this question has no answer. This is because special relativity postulated (and we have experiments for that!) that there is not "special" reference frame that "is not moving".
Before Einstein it was assumed that there is a special medium named ether, that would be that special reference frame, and if this was the case you could always measure your speed in reference to ether using simple physical experiments: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment .