An object of mass $2\, kg$ is sliding with a constant velocity of $4\, m\, s^{-1}$ on a frictionless horizontal table. The force required to keep the object moving with the same velocity is (in $, N$)

$A$ man is at rest in the middle of a pond on perfectly smooth ice. He can get himself to the shore by making use of Newton's:

$A$ motor car is moving with a velocity of $108 \, km \, h^{-1}$ and it takes $4 \, s$ to stop after the brakes are applied. Find the force exerted by the brakes on the motor car if its mass along with the passengers is $1000 \, kg$.

What force would be needed to produce an acceleration of $4 \, m s^{-2}$ on a ball of mass $6 \, kg$?

Why is it advised to tie luggage with a rope on the roof of buses?

$(a)$ State the law of conservation of momentum.
$(b)$ Mention two factors which determine the momentum of a body.
$(c)$ Prove the law of conservation of momentum with clear explanation,diagram and equation.