zaostati

1. (in movement) to fall behind; to drop back
   Zaostao sam za grupom jer sam stao da slikam. — I fell behind the group because I stopped to take photos.
   Biciklista je zaostao nekoliko minuta. — The cyclist fell a few minutes behind.
2. (za + instr.; in progress) to lag behind; to fall behind
   Dete je zaostalo u školi zbog bolesti. — The child fell behind at school because of illness.
   Zaostali smo s plaćanjem kirije dva meseca. — We fell two months behind with the rent.
3. (of things, traces) to be left behind; to remain
   Posle poplave je u podrumu zaostalo blato. — Mud was left in the basement after the flood.

The person or thing one falls behind is expressed with za + instrumental: zaostati za nekim.