This app was mentioned in 6 comments, with an average of 2.17 upvotes
Data-logging:
Video comes from a GoPro and the overlay is done with Dashware. RaceChrono can export data in a format that Dashware understands.
For me it is a free app. You can download it and test what you can do with it. I don't have much experience with it since I don't use it at all. Maybe some lap time apps could do the same job
Cant the student or her put the cellphone on the back pockets of the front seats?
If so, there are tons of Android apps, heck, even an old, used beated up anything 4.1 or better Android would be good for that, lots of apps used to time laps, and they have learning mode to memorize the track, put it in new track mode, lock display and off you guy.
From example RaceCrono will do that:
https://play.google.com/store/apps/details?id=com.racechrono.app
Or even the Pro version at 20$ will be cheaper than a dedicated GPS tracker.
For anyone interested in doing this, I've run this setup for the last few years and it's awesome. Upload your telemetry on serious-racing.com and compare with your friends (my username is 'shadoop' if you're in CA or FL and want to add me) . Very accurate (tested against traditional track system). Setup: Phone - GPS - App
There are loads of them, Race Chrono for example.
Some action cameras even have circuit overlays.
Then there are the expensive solutions like Vbox, which are great if you need more accurate data from your car.
I use Race Chrono when on track and find it very good
https://play.google.com/store/apps/details?id=com.racechrono.app&hl=en