Question

a train is moving on horizontal rails with a uniform acceleration 5m/s2. a passenger siiting in a boggie drpos a stone inside the boggie. what will be the acceleration of stone wrt the rails??

Answer 1

Once the stone leaves the passenger's hand, its horizontal acceleration
stops.  Its horizontal speed after that is whatever horizontal speed it had
at the instant it was dropped. 

Its vertical acceleration ... its total acceleration with respect to the rails,
is 9.8 m/s² straight downward ... the acceleration of gravity.