Why dose battery light come on in high rpm from stop after 4rpm in first gear?

97 ford Taurus 3.0L. Battery light comes on when I accelerate from a stop to 5k rpm first gear 60mph ish. All light that are on get 2x brighter and after 30 sec all the lights go back to normal and battery light turns off after i stop accelerating and slow down to 40mph at 2-3 rpm. Why is that?

Your alt. Is going out.

Get the alternator load tested. It is likely failing.

Probably loose alternator belt… Or worn out brushes in the alternator.

I'd suspect your voltage regulator is on its way out if I'm reading your description of the symptoms correctly (brighter than usual lights at higher engine speeds). I believe the regulator is mounted on the alternator itself for your particular car. Often when the regulator goes bad, the alternator is replaced at the same time. If it's not the regulator or some other problem with the alternator, then the battery itself is the next thing I'd check.

** If the battery is making any noise prior to testing/inspecting (bubbling/gurgling/hissing) or if you can feel substantial heat coming off of it with your hand near it (but not touching…), stay the heck away from the battery until it has a chance to properly cool down. ** You may also notice signs of corrosion near where the battery sits - if so, that's often another sign of a bad voltage regulator because it can cause the battery to overheat and off-gas substantially (which is where the sounds would be coming from). Batteries don't often explode but you definitely do not want to be anywhere near it if it does so exercise caution if you decide to look into the battery condition and you have a suspicion that it's been getting overcharged.

Voltage regulator is malfunctioning.

The alternator and power steering pump is a "weak spot"!
Meaning that one reason Ford puts the redline where it does is because these parts fail when operated at high RPM's too often. The failure is often in the brushes, but also the voltage regulator sometimes just can't regulate like it should.
It is my habit to replace both when this happens. An alternator failure can cause a voltage regulator failure and the reverse is also true. I hate to replace one only to find out I either replaced the wrong half of the problem or that I should have got them both the first time. If you replace the wrong part of the problem, the replacement part will soon fail and have to be replaced twice.

Hi so did it get that high in RPM. It';s a wonder it didn't explode.

Get the battery and charging system tested. Auto parts stores do that for free.