Rear Ended on Freeway

I was driving along the freeway with the speed limit at 70 mph, and I
was going about that fast. The lady in front of me slammed on her
brakes HARD. It was so hard that by the time I hit her car I couldn't
see it because of all the smoke from her tires. I was maintaining a
safe following distance (3 seconds), but it was still not enough time
for me to stop my car. The officer claimed it was my fault because I
didn't give her enough room. I don't think I should have to pay for the
extensive damage on my car. Any thoughts from anyone?