On this page of the Cyberpunk 2077 guide, you will find a walkthrough for the Human Nature quest. You will find out when Jackie's vehicle will be unlocked and what to do after the car is damaged by a cab.
How to start the quest: This quest will be automatically added to your log after completing act 1 of the campaign.
The car, which belonged to Jackie, has now become the property of V. You have to reach the garage adjacent to the character's apartment to pick it up. After you get in the car, your new machine will be rammed by an AI-controlled cab.
AI Delamain will contact you to apologize and promise to repair the car and pay compensation - the latter will start a new side quest Tune Up.
You don't have to do anything else with this quest. You just have to wait until repairs are completed. You will receive a text message from Delamin, and a confirmation that the Hella EC-D I360 vehicle has been unlocked. You can already select it from the list of machines of V.