Justify giving proper reasoning whether the work done in the following case is positive or negative: Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.

Given below are a few situations. Study them and state in which of the given cases work is said to be done. Give a reason for your answer:
$(i)$ $A$ person pushing hard a huge rock,but the rock does not move.
$(ii)$ $A$ bullock pulling a cart up to $1 \, km$ on the road.
$(iii)$ $A$ girl pulling a trolley for about $2 \, m$ distance.
$(iv)$ $A$ person standing with a heavy bag on his head.

Is it possible that a body be in accelerated motion under a force acting on the body,yet no work is being done by the force? Explain your answer giving a suitable example.

$A$ boy throws a rubber ball vertically upwards. What type of work is done: $(a)$ by the force applied by the boy,and $(b)$ by the gravitational force? Support your answer with reasons.

$A$ car and a truck are moving with the same velocity of $60\, km h^{-1}$. Which one has more kinetic energy? (Mass of truck $ > $ Mass of car).

The potential energy of a person is minimum when: