Justify,giving proper reasoning,whether the work done in the following case is positive or negative: Work done by gravitational force when a bucket is pulled upwards.

One joule of work is said to be done when:

In case of negative work,the angle between the force and displacement is: (in $^o$)

$A$ man of mass $60 \, kg$ runs up a flight of $30$ steps in $40 \, s$. If each step is $20 \, cm$ high,calculate the power of the man.

What is the amount of work done by a force when a body moves in a circular path?

$(a)$ State the law of conservation of energy.
$(b)$ What is the work done to increase the velocity of a car from $36 \, km/h$ to $72 \, km/h$ if the mass of the car is $1500 \, kg$? Does the work done by the force have a negative or a positive magnitude?
$(c)$ Where does an oscillating pendulum have maximum potential energy $(PE)$ and kinetic energy $(KE)$?