Let us consider body moves a distance S due to the force F.
Hence the work by the body W = FS
If the force is not along the direction of displacement,then the work by a body for travelling a distance S will be -
where
is the component of the force along the direction of displacement.


As per the question the power P is given as -




Hence alternative definition of power P = F.V
Yes.
The acceleration vector WILL point south when the car is slowing down while traveling north
The equivalent of the Newton's second law for rotational motions is:

where

is the net torque acting on the object

is its moment of inertia

is the angular acceleration of the object.
Re-arranging the formula, we get

and since we know the net torque acting on the (vase+potter's wheel) system,

, and its angular acceleration,

, we can calculate the moment of inertia of the system: