How are kinetic energy and momentum related?

$(i)$ State the law of conservation of energy.
$(ii)$ Show that the total mechanical energy of a freely falling body is conserved.

$A$ body of mass $4 \, kg$ initially at rest is subjected to a force of $16 \, N$. What is the kinetic energy acquired by the body at the end of $10 \, s$ (in $, J$)?

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

$(a)$ 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 $(KE)$?

State whether the following statement is true or false:
When a body falls on the ground and stops,the principle of conservation of energy is violated.