Do we know if the car is actually moving at full speed and not at casual speeds?
To determine whether or not the car is moving a casual speeds. We must define casual speeds. To my understanding casual speeds refers to the speed of a car given the traffic conditions, which could be higher or lower than the legal speed limit, correct?
If that is the case, then we must look at that manga panel/anime. For instance, we can see that there are no vehicles in sight.
Comparison:
Here we can see that there is no traffic, no speed sign, enforcement presence:
Here is another example in the manga, but there are thing that could influence a driver's speed. In the image below, we can clear see many pedestrians on the sidewalk and even police officers car parked, so if a car were to drive trough that road, then they most likely will be going lower than the speed limit.
Given that there are practically no factors that could have impacted the driver's speed, my conclusion would be that driver would be going at least the speed limit or higher.
Potential counter argument: "Well Shinichi was on the side walk that could have affected the drivers speed." To address that in the manga panel, shinichi is leaving the hotel, so the car must have been ahead of him. Additionally, we do not see people outside. The old man and girl are inside the hotel, so they could not have impacted the drivers speed. Lastly, given the manga's intent(which is to showcase Shinichi's superhuman abilities), there is not reason for the driver to be going slower.