You have the possibility to acquire vehicles in Dragon Ball Z Kakarot if you have the necessary parts and zenis. Their use is almost limited to a few speed races since everyone can fly much faster, but let the collector in you speak before you go back to sub stories. Vehicles can also help you collect ore, but this is rather anecdotal.
Build a vehicle
During the Android and Cell Sagas, go to the R&D section of Capsule Corps in the West City, you can buy the vehicles and upgrade them in exchange for zenis and adapted parts. Parts that you probably don't have, since you have to combine components and zenis to get them. So it's a step-by-step process. You can create these vehicle parts in the second tab. You will have to create all the vehicle parts, one by one.
What you'll need in large quantities is Iron, you need about 60 just for the car, you can easily mine some in the Desolate Lands of Gizard, east of the Central Plains Zone map. Mine anything you come across, then leave the map, or save and load. You can also use NPC comments to help you find out when there's Iron nearby.
Vehicle parts
Things get complicated for other components such as axles. To obtain them, it will be necessary to search the car bodies scattered on the different maps. The good news is that they are usually near an NPC with a bubble. Here is the position of several of them.