What is the formula for objects crossing my path?

Question

When I stop my car at a traffic junction, watching out for oncoming traffic, I judge in a split second if it is safe or not to cross the road. This judgment includes the acceleration of my own car and the varying speed of approaching traffic. What would a workable formula be to determine this theoretically? I there is the basic formulas available but it does not answer my question completely

Answer 1

Answer 1 gives a good outline of the formula one might apply in a retrospective analysis. But I don't think you do square roots and algebra while driving! I think it's more applying your stored memories of acceleration to this situation, in a kind of pseudo simulation.
First, you know there's a hypothetical collision point in the far lane of the cross traffic, ahead of you if you're crossing, more toward your left if you're entering it. From experience you know how fast you can reach that point. If that's long enough before the other car, traveling at more or less constant speed, then go; else wait for another chance.
Something like that.

Answer 2

The formula used by your mind is t1 = √(2d/a). t1 is the time for you to clear the distance d across the intersection. Then it computes the time it will take the approaching traffic to reach the path of your car, t2 = V(est)/D where D is the distance of the traffic from your crossing point. As long as t1 is less than t2, a safe crossing can be negotiated.
These numbers are not fixed, however. D is constantly decreasing and V(est) is just your perception of the speed of the traffic. Likewise, a and d are only guesses by you based on your driving experience...
Makes a person wonder how we stay alive! A large dose of safety factor applied probably helps.