I'll leave this for someone else! Too easy for me.
Sorry, couldn't resist. Sears Allstate Special (my daughter used to work for Allstate, and I am not a fan of the company - I'll say no more for fear of litigation). Designed and built by the legendary Mickey Thompson - this looks like a test session for the typically Thompson innovative bodywork, what with the tufts attached to the car. If it's 1963 then it's got a Chevrolet engine, if it's '64 then it's a Ford.
Many top drivers refused to get into these cars. Before the start of the '64 Indy 500 Masten Gregory had a chat with Jack Brabham who had been placed alongside poor Dave MacDonald's car on the grid. He advised Jack to stay well clear, which Jack did, and afterwards he said Masten's advice saved his life.
(I've just checked race numbers - the puzzle photo is actually Dave MacDonald at the 1964 Indy 500. I've no idea why the car is fitted with streamlining tufts, unless they were checking problems during qualifying or testing. My source reckons Jim Clark said to Dave "Don't get in that car". I cannot explain my personal hatred for that car - I wasn't some sort of fan of MacDonald, and I admired Mickey Thompson as an American version of Colin Chapman - brilliantly talented but with a penchant for refusing to accept he was wrong. )