Avinash can run with a speed of $8 \, m \, s^{-1}$ against a frictional force of $10 \, N$,and Kapil can move with a speed of $3 \, m \, s^{-1}$ against a frictional force of $25 \, N$. Who is more powerful and why?

$(a)$ What is meant by mechanical energy? State its two forms. State the law of conservation of energy. Give an example in which we observe a continuous change of one form of energy into another and vice-versa.
$(b)$ Calculate the amount of work required to stop a car of $1000 \, kg$ moving with a speed of $72 \, km \, h^{-1}$.

What is the work done by a coolie walking on a horizontal platform with a load on his head?

$(i)$ An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the total work done against the force of gravity and by the force of gravity on the object? Explain with proper mathematical expression.
$(ii)$ $A$ certain force acting on a $20 \, kg$ mass changes its velocity from $5 \, m s^{-1}$ to $2 \, m s^{-1}$. Calculate the work done by the force.

The potential energy of a person is minimum when:

State whether the following statement is true or false:
$A$ force does not work, if it produces no motion.