Suppose you are sitting on an accelrating trolley car.
(i) Find the pseudo force action on the block of mass m placed on the trolley car.
If the block is placed (or moved) outside the trolley car, and an external force F acts in horizontal direction.
(ii) Find the pseudo force acting on the block as viewed by the observer.
(iii) Find the acceleration of the block as seen by the obersever

Explanation

In each case of pseudo force will act oppsite to the direction of acceleration of the observer. It is equal to `vecF_(pseudo)=-mahati`
If a horizontal force starts acting on the blocks the FBD of block with respect to observer,
Then acceleration of the block w.r.t. observer
`a_(m,observer)=(F_(pseudo)+F)/(m)=(ma+F0/(m)=a+(F)/(m)`
Hence `veca_(m,observer)=-(a+(F)/(m))hati`