$A$ spring which has been kept compressed by tying it is allowed to be dissolved in an acid. What happens to the potential energy of the spring?

$(a)$ 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 $(KE)$?

$(a)$ 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 $72 \, km \, h^{-1}$.

$(a)$ $A$ person is holding a bucket of water by applying a vertical force of $100 \, N$. He first moves a horizontal distance of $5 \, m$ and then climbs up through stairs a vertical distance of $10 \, m$. Calculate the total work done by the person on the bucket.
$(b)$ Establish the relationship between kinetic energy and momentum of a body.

$A$ body of mass $5\, kg$ initially at rest is subjected to a force of $20\, N$. Find the kinetic energy acquired by the body at the end of $10\, s$. (in $, J$)

Two children $A$ and $B$ each weighing $20 \, kg$ climb a rope up to a height of $10 \, m$. Child $A$ takes $10 \, s$ and child $B$ takes $20 \, s$ to climb. State whether the work done by both is equal or unequal. Who has more power?