Drive performs this function in English, it can be used both for persons
2 a : to operate a vehicle
// learned to drive at the age of seventeen
b : to have oneself carried in a vehicle
// drove to Canada as a kid
(source: Merriam-Webster)
and for the vehicles themselves:
- To move along or advance quickly: We could hear the trucks driving along the highway.
(source: The Free Dictionary)
For some vehicles, ride works as well, but it's almost never used with a car:
1 a: to travel on
// ride a bike
// ride the bus
(source: Merriam-Webster)
Your example would become:
Imagine a car driving down the way, and then it stops gently.