I think in this case it’s possible to give a reasonable answer to the question “Why?”, as follows:
When a body moves through a fluid, it imparts motion to the fluid, which costs energy. The amount of motion in the fluid - and thus the energy lost by the moving body - will increase as the speed of the body increases.
How does saying, “Because that’s the way it is,” benifit the OP?
zut’s already nailed it, basically that the drag coefficient, and therefore drag force, is proportional to the velocity squared.
This is mostly because constantly changing speed usually requires lots of braking (i.e, stop and go traffic). Unless you have a hybrid with regenerative braking, any time you step on the brake pedal, you’re wasting energy ( the momentum you had stored while moving is changed into heat & sound via brake friction).
If you are able to correctly anticipate “stop-and-go” traffic enough to “coast” instead of alternating throttle/brake, your mileage goes way up as well.
That’s true, but coasting and accelerating will still give you worse gas mileage than driving at a constant speed. Newton’s first law and all (IOW, it takes more energy to accelerate a car than it does to keep it going, and you don’t get that energy back when you’re coasting).
ETA: His second law as well:
1 A physical body will remain at rest, or continue to move at a constant velocity, unless an outside net force acts upon it.
2 Rate of change of momentum is proportional to the resultant force producing it and takes place in the direction of that force.
That’s not really the reason, though, because the energy taken to accelerate is stored in the kinetic energy of the car, and you do get that energy back, through not needing to engage the engine to keep moving forward while coasting.
As to how fuel efficient accelerating/coasting is, it would depend on what vehicle speed range you’re operating in (i.e., where the energy is being dissipated) and what engine speed/load range you’re operating in (i.e., how efficiently the energy is being produced from gasoline).
As a thought experiment, I can imagine a “hybrid drive” cycle where you start the engine up, run it at a highly efficient point, and store the output energy in the form of kinetic energy (i.e., “accelerate”), then shut the engine off and run on stored energy (i.e., “coast,” sort of). This of course ignores the changing losses due to changing vehicle speeds, but point is it’s not necessarily inefficient to do this.
You’re going to have a doozy of a time explaining yourself on that one. You can’t just cite “Newtons 1st law” and handwave the rest away.