A) No, the equations presented above are the product of the derivation of position and velocity when the acceleration is constant.
The equations change to polynomial function of the second degree for the description of the acceleration when described as a function of time.
B) Yes, when the acceleration is zero it is concluded that the velocity is constant, therefore they could be used to describe the position as a function of the change in velocity.
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This isn't a physics question really, but you should slow down unless you don't believe you can stop in time or don't believe it is safe to stop quickly (say you see someone driving very close behind you and you don't think they're paying attention). In general, if you think that by staying at your current speed your back tires will cross the ending lines of the intersection by the time the light turns red, it is safe to go through the yellow light. However, this is a thing you'll develop a feel for as you're driving, when in doubt, just slow down, just watch slamming on your breaks if there is someone behind you, sometimes people will see the yellow light when they're behind you and they'll speed up behind you so they'll "make it" before the light turns yellow. While this isn't illegal, since they're not technically running the red light, you should never speed up going up to a yellow light, if you need to speed up to make it before it turns red, you shouldn't make the light, just stop, this is especially bad if someone is directly in front of you and is likely to stop at the yellow light while the person behind them speeds up. This causes a lot of accidents.
