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Related to jog on: jog memory
1. Literally, to run along at a slow and deliberate place. We were running a little late for class, so we jogged on from the library toward the lecture hall.
2. By extension, to make progress slowly, deliberately, or patiently. Though the economic downturn hurt the company's profits, we've been able to keep jogging on until things begin to improve.
3. Go away; get lost; beat it. Primarily heard in UK. Jog on, you lout! Quit disturbing our customers!