Life in US: How to avoid a tailgate accident?

I had two tailgate accidents in a month. Fortunately, my car only had minor damages. Nothing bad.

One raining day when I was heading a cross, the light turned yellow. I stopped and felt I was pushed by someone. When I check my rear mirror, a truck was just backing from my car.

I stopped and got down to check possible damage. Noting except some scratches. I pardoned the guy, who was about in his sixties.

Another day, I was driving to a farm. When I made signal to turn left and slowed down, my car was jumping ahead heavily. It was shock to me and my family. After stopping, I checked my car "carefully", but did not find any damages. God bless. The lady who pushed my car,also in her late fifties, was so scared that she put her hand on her heart and was hard to breathe...

I let her go and afterwards I found my rear bumper sank. My daughter, who was seated in the back, felt uncomfortable...but not serious, Thank God.

Is it wise to take done her driver's license and phone number?