Careless driving in nj with accident?

Right before christmas coming up to the deptford mall, traffic was at a standstill. from a dead stop, as i began to accelerate again, the lady( who was on a cell phone, may i add) infront of me put her brakes on hard, and i slammed mine on and hit her in the rear at 20mph( speed limit is 55, but as i said, we were at a standstill). Her car had a few scratches on the bumper, while mine required $2000 in work because i hit her with the un-reinforced parts of my car( my car was lower than hers) when the officer showed up, he served me with a careless driving ticket. when i asked him why he said it was because i hit her. Do i deserve this ticket or should i fight it. at the end, she drove away with no problems while i had to limp my car back home, held together with wire ties. any help/advice is welcome.