Learn Polish: Samochód jechał w kierunku Krakowa. - The car was driving towards Kraków.

The phrase w kierunku literally means 'in the direction'. Because you are saying 'in the direction of Kraków', you need the Genitive case (the 'of' case) to connect the nouns, which turns Kraków into Krakowa.

What case is kierunku in the phrase w kierunku?

It is in the Locative case. The base word for direction is kierunek. The preposition w (in) takes the Locative case here. When forming the Locative, the movable 'e' drops out and we add -u, making it kierunku.

Why does this sentence use the imperfective verb jechał instead of the perfective pojechał?

Jechał focuses on the ongoing process of driving at a specific moment in the past (was driving). If you used pojechał, it would mean the car set off for or successfully drove to Kraków, rather than just describing the direction it was moving in at the time.

Could I just use do instead of w kierunku here?

You could say do Krakowa, but that translates to 'to Kraków', implying Kraków was the actual destination. W kierunku Krakowa specifically means 'towards' or 'in the direction of', which is more precise when describing the path rather than the destination.