Change in speed = (acceleration) x (time)
4 minutes = 240 seconds
Change in speed = (40 m/s²) x (240 seconds)
Change in speed = 9,600 m/s
What you're actually describing here is a car pulling 4 G's for 4 minutes, and ending up going 21,475 miles per hour.
The driver would definitely NOT get a speeding ticket, because nobody could catch him.
Also, his car would heat up and shoot flames from atmospheric friction.
(He could avoid this with some fancy steering, leave the atmosphere, and end up in low-Earth-orbit.)
Actually, I hope there's nobody in the car. His experience wouldn't be pretty.