What kind of physics does a police officer need for investigating car accidents?

K=½mv² is about as complex as it gets for either. Physics isn’t the hard part about forensics though.

You are looking for the branch of physics called Dynamics. It deals with motion, forces, and equilibrium of single or multiple masses.

Honestly though physics rarely come into the equation with car accident investigations. In most cases the officer is only trying to determine who’s at fault for the accident. Physics don’t really help establish who had the right-of-way and who ran the red light.