That is just what happened when Byrd murdered Babbitt. He stalked her. At least the ICE agent did not stalk the woman he shot but she stalked him using her car.His split seconds would have been better spent getting out of the way (not difficult since he was just on the corner of the front bumper) rather than taking her life.
But that decision making is going to be influenced by one's state of mind. If you want to kill someone, that will definitely be your first instinct.