Justify,giving proper reasoning,whether the work done in the following case is positive or negative: Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

$(a)$ State the law of conservation of energy.
$(b)$ Establish the relation between the $SI$ unit of energy and the commercial unit of energy.
$(c)$ $A$ toy car is displaced through $5 \, m$ on the application of a force of $7 \, N$. Assuming the force acts on the object throughout the displacement,what is the work done in this case?

$(a)$ Define work. State two factors on which the magnitude of work depends.
$(b)$ $A$ car and a truck have the same speed of $30 \, m/s$. If their masses are in the ratio $1:3$,find the ratio of their kinetic energy.

State whether the following statement is true or false:
When an arrow is released from a bow,potential energy changes into kinetic energy.

When a stone of mass $m$ falls through a vertical height $d$,the decrease in the gravitational potential energy is:

$(a)$ Define the term 'average power'.
$(b)$ When a player hits a football,it moves along a curved path and then falls to the ground. Calculate the work done by the force of gravity on the football.
$(c)$ Two friends,Ram and Shyam,each having a mass of $40 \, kg$,go for rock climbing. Ram climbs to a height of $3 \, m$ in $10 \, s$ and Shyam covers the same height in $12 \, s$. Is the work done by Ram and Shyam equal or not? Compare the power of Ram and Shyam.