$A$ man weighing $60 \ kg$ runs along the rails with a velocity of $18 \ km \ h^{-1}$ and jumps into a car of mass $1$ quintal $(100 \ kg)$ standing on the rails. Calculate the velocity with which the car will start travelling along the rails. (in $m \ s^{-1}$)

$(a)$ State Newton's second law of motion and show that the first law of motion can be mathematically derived from the mathematical expression for the second law of motion.
$(b)$ A stone dropped from a window reaches the ground in $0.5 \, s$ (given $g = 10 \, m \, s^{-2}$):
$(i)$ Calculate the speed just before it hits the ground.
$(ii)$ What is the average speed during $0.5 \, s$?
$(iii)$ Calculate the height of the window from the ground.

What is the $SI$ unit of force?

$A$ jet engine works on the principle of Newton's:

$(a)$ Define inertia. You are provided with three bodies made of wood,rubber,and iron of the same shape and size. Which one of them will have greater inertia? Explain it.
$(b)$ When a striker hits the bottom of the pile of coins placed at the centre of a carom board,only the lowest coin is removed. Give reason for it.

$A$ 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 $1000 \, kg$.