UMath1 said:
The car would remain in the lane beside me as it sped forward.
If you were moving at highway speed and the other car "sped forward", or sped by you, I would say it is likely that he had a fairly significant speed delta relative to you initially. There are exceptions, but at freeway speeds most cars are not able to accelerate very quickly due to various factors (wind resistance, gearing ratio). If he was sitting in your blind spot matching your speed for even a short time, and his car had a lot of power, he could have accelerated relatively quickly. But even so, the distance from your blind spot to a position where you could see him out your window is a relatively short distance. So even a fairly powerful car could not accelerate a great deal in that short of a distance. If he was accelerating hard, were you able to hear his engine roaring? Then again, I suppose the reason you are asking is that this was some kind of a traffic incident, in which case you (or the person involved) probably didn't hear him.
Obviously, if it was at lower speeds on city streets, the other car could accelerate more quickly. But even if he did accelerate quickly, if this is a "who's at fault" kind of issue, I'm sorry to say it, but I don't think you have a good case if you changed lanes and hit him. Then again, I'm just speculating as to why you are asking about this.
If you were shown a very short snapshot in time (a very small fraction of a second) of another car relative to your car, you could probably estimate its distance from you fairly accurately. But if you were asked to estimate acceleration, or even speed, you would need to observe it for a longer time to be able to observe change over time. When I had the opportunity to use a radar gun, it had an audible tone that increased or decreased pitch as the car's speed increased or decreased.