State Newton's first law of motion.

$(a)$ 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.

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

The inertia of an object tends to cause the object

State Newton's third law of motion.

The quantitative definition of force is given by