You're probably right. I just remember a series of school physics lessons where we measured the acceleration of a toy 'matchbox' car on a wooden ramp about a foot long so we could time the speed increase per distance and vaguely recall acceleration being a square of velocity. This is why I said (sort of) that the car picks up momentum as a square. Same analogy as braking distances being a square of speed. If you're going twice as fast, you need more than twice the braking distance. We just got reminded of this on my recent speed awareness course when they told us that we'd surely kill someone if we went over the speed limit.
There's no doubt in my mind however, that two cars travelling at the same speed at a given point in time can have dramatically different momentia, (if that's even a word), as one can still be overcoming inertia to attain a given speed while the other can be braking to shed momentum. 40 mph for example, is just the snapshot point at which their respective speeds cross, with their stored energy ramping in different directions. This is my point, basically.
Imagine braking from 180mph down to zero as fast as you can. The car will still be lurching forward when the front tyres finally stop dead. It then rests back down level as the tyres and suspension absorb the remaining momentum.
Now imagine it coasting smoothly to a stop over a much longer distance, say a mile. The car will just appear (and feel) to stop without any forward momentum to speak of because the momentum has been dissipated in line with deceleration. Speed and momentum are two seperate phenomena, the latter causing many back ends to swing out when it isn't killed properly and why you shouldn't brake during a corner but before. You need to kill the car's momentum as it isn't directly proportional to speed. There's a distinct lag time. This is why it's unnerving to drive with someone who brakes too late because you can feel the car's momentum pushing you forward strongly, even at slow speeds, making you doubt that you're going to stop in time.
Once scientists understand gravity, they'll be up to speed.
Mass for example, is not a constant. Acceleration increases mass, otherwise, standing on a set of bathroom scales, you wouldn't be able to make the weight reading increase by bending your legs quickly then stopping. You've gained mass or energy by moving faster. That's momentum.