Ajar can be an adverb or adjective describing something as being partially open.
An archaic and obsolete definition for ajar is for something to be out of sync with its surroundings or to be jarred.
The a- prefix is often used in words as a stand in for to (aside means to the side), in (as in the process of or in a certain condition), or on (e.g., if someone is walking afoot, he or she is walking on foot). This comes from the simplification of the Old English two word phrasing.
Afoot may mean to be traveling by use of one’s feet. However, this definition is rarely used. The more common definition is that something is starting or being prepared. The famous example is Sherlock Holmes saying, “The game is afoot.” Or “The game is beginning.”
He saw the passenger-side back door was ajar, and there were some tools missing. [Wisconsin Rapids Tribune]
The on-camera reactions to the jokes were mixed — some of the stars in the audience, like Jessica Chastain, sat with jaws ajar, while others, like George Clooney, could be seen laughing. [Local 10]
Now, changes are afoot to tighten remaining campaign finance regulations in Montana, and Commissioner of Political Practices Jonathan Motl has been active in enforcing existing ones. [Missoulian]
It’s clear that some part of Malcolm suspects shenanigans are afoot, but nonetheless, he agrees to meet David for a prisoner exchange later that night. [Entertainment Weekly]
From Portsmouth, they traveled afoot to Columbus, thence to Mount Vernon, thence through Mansfield to Tiffin, to which place they were recommended by people in Portsmouth. [Mansfield News Journal]