Yup. That is a Norelco “Auto Mignon".

The Philips Mignon (branded Norelco in the US) was surprisingly long-lived, produced from 1958 through 1970. It didn’t need specially-made records; 45 rpm records were simply slid into a slot in the front, a futuristic development 40 years ahead of in-dash CD players. However, the unit held only one record at a time. You needed to jockey a lot of singles to provide continuous music on any drive longer than around the block. The Beatles reportedly each had one in their cars, and George Harrison was also photographed using one in his Jaguar E-type.

Can't find the exact price but the best I can tell is that it cost about $500 in today's dollars.

The turntable was spring mounted and there was increased downward stylus pressure to prevent skipping and according to Consumer Reports, when the magazine tested the Auto Mignon and other similar players in the early 1960s, the Auto Mignon did not skip even in adverse road conditions. However, concerns were raised regarding premature record wear due to the extra pressure on the stylus.

I can't link to it directly because the spam filter in this sub deletes comments with external links, but the following incomplete link, which can be copied and pasted to your browser, goes to a video that shows one playing a record while being shaken:

youtube.com/watch?v=aKfaEb1n2F4

Skip to about 6:25 to see the demonstration.