Or they might log the speed every n seconds and store it in a file for a program to analyse later.

This is the more typical use case. Managers/safety officers will want a report of "who sped the most in the last X days" both in terms of highest speed and average over-the-limit driving. In extreme circumstances, such as when onboard sensors detect an impact or impending rollover, the logging can ramp up to multiple times per second. Great for insurance purposes.