Learn Russian: Машина подъезжает к перекрёстку. - The car is driving up to the intersection.

The prefix под- means "approach" or "move up to." However, because a car (машина) drives on wheels rather than walking on foot, we use the vehicle-based root -езжать (from ехать) instead of the foot-based root -ходить.

Why is there a hard sign (ъ) in the middle of подъезжает?

In Russian spelling, when a prefix ends in a consonant (like под-) and the root starts with a "softening" vowel like е, ё, ю, or я (like -езжать), you must insert a hard sign (ъ). This prevents the sounds from blurring together, keeping the "d" sound hard and separate from the "ye" sound.

Why is the noun перекрёстку in the Dative case here?

The preposition к (meaning "towards" or "up to") always requires the Dative case. When using prefixed verbs of approach like подъезжать or подходить, they are almost always paired with к + Dative to point out exactly what is being approached.

The dictionary form is перекрёсток. Why does the "о" disappear in перекрёстку?