When a speeding bus stops suddenly, passengers are thrown forward from their seats because 

the back of seat suddenly pushes the passengers forward. 

inertia of rest stops the bus and takes the body forward.

upper part of the body continues to be in the state of motion whereas the lower part of the body in contact with seat remains at rest. 

upper part of the body come to rest whereas the lower part of the body in contact with seat begins to move.