A railway carriage moves over a straight track with acceleration a. A passenger in the carriage drops a stone. What is the acceleration of the stone w.r.t. the carriage and the earth?

[prasanna]

When the stone is dropped, it falls freely under the acceleration due to gravity g. With respect to the earth the acceleration of the stone is g
Inside the carriage the stone possesses two accelerations:
(i) Horizontal acceleration V due to the motion of carriage.
(ii) Vertical downward acceleration ‘g’ due to gravity. The acceleration of the stone w.r.t. the carriage.