My Grandfather's car. 1929 Whippet. Produced by Willys-Overland Motors, an American automobile company best known for its design and production of military Jeeps and civilian versions during the 20th century. In 1926, production of the Whippet car began. Following the stock-market crash of 1929 and the economic depression that soon followed, a number of Willys automotive brands began to falter. Whippet production ended in 1931.