What are Eckels's motives in going on the safari into the past?
Eckels's motive to go on a time safari to the past is to hunt and shoot a dinosaur.
From the beginning of the story, Eckels is full of pompous arrogance. He saunters into the safari company and slaps down his big check. He barely listens to the rules about traveling into the past, and he brags about all of the other safaris that he has been on. Once in the past, he playfully aims his gun at all kinds of imagined targets. He even firmly states that he is there to shoot "my dinosaur," even though he is one of several hunters hunting that particular dinosaur. Unfortunately for the present/future, Eckels winds up being a complete coward. He steps on and kills a butterfly. The effects ripple through time, and the entire societal structure of the present/future changes.