Question

Why do the passenger in a bus lean forward when suddenly brake is applied

Answer 1

because while the bus in motion and passenger is to be at rest due to inertia of rest we may fall forward .

Answer 2

Due to inertia of motion, the passenger's body remains in motion alongwith the bus but as the bus stops, the passenger's body maintains it's motion due to inertia of motion. So the body sways forward.