I disagree with you regarding resolution and frame rates, I don't see why you would need a high speed camera. Something like a raspberry pi camera would be perfectly sufficient for this, assuming you still just want to get someone's speed to within say +/- 1mph to shame them, as in the original comment.

Set up your RPi camera about 20m from the road, with it's FOV that'll give you about 20 m of road coverage. Rule of thumb in my world is that the items of interest should not move more than 1/4 of window width between frames. So that's 5m, to move 5m between frames at 30Hz you'd need to be doing about 300 mph. More realistically the car might be doing 25m/s giving you an inter-frame displacement of 0.8m ~130px. If that's too little for your software to register just up the inter-frame time.