Learn Russian: Я качу эту тяжёлую бочку прямо на склад. - I am rolling this heavy barrel straight to the warehouse.

Катить is the unidirectional verb for rolling or pushing an object. Because the speaker is rolling the barrel in one specific direction toward a clear destination (на склад), we use the unidirectional verb. If they were rolling it back and forth or aimlessly, we would use the multidirectional катать.

The infinitive is катить, so why does the я form use a ч in качу?

This is a standard consonant mutation. In second-conjugation verbs ending in -тить, the т changes to ч only in the first-person singular (я) form. The other forms keep the т, such as ты катишь and он катит.

If the barrel were rolling down a hill on its own, how would the verb change?

You would need to use the reflexive version of the verb, катиться. For example, Бочка катится на склад means the barrel is rolling to the warehouse on its own. Here, because someone is actively rolling an object, we use the transitive non-reflexive verb катить.

Why do we use на склад instead of в склад if a warehouse is usually an enclosed building?