Learn Russian: Бегуны должны безопасно переходить улицы.

The prefix пере- generally means 'across' or moving from one side to another. When added to ходить (to walk or go on foot), it creates переходить, which means 'to cross' on foot.

Why is the imperfective verb переходить used here instead of the perfective перейти?

We use the imperfective переходить because this sentence describes a general rule or a repeated, habitual action: runners in general must cross streets safely. If this were a single, specific crossing being completed, you would use the perfective перейти.

Why do we use должны instead of just должен?

Even though it translates to the English verb 'must', должен behaves like a short adjective in Russian, so it has to match its subject. Because the subject бегуны (runners) is plural, we use the plural form должны.

Is улицы in the nominative or accusative case here?

It is in the accusative plural case because it is the direct object of the verb (the thing being crossed). For inanimate nouns like streets, the accusative plural is identical to the nominative plural, which is why it looks exactly the same as the basic plural form.