State Newton's second law of motion.

$(a)$ $(i)$ Define momentum. State its $SI$ unit.
$(ii)$ An object of mass $50 \ kg$ is accelerated uniformly from a velocity of $4 \ m/s$ to $8 \ m/s$ in $8 \ s$. Find the magnitude of the force exerted on the object.
$(b)$ State Newton's first law of motion.

Amar, Javed, and Rita were riding in a bus that was moving with a high velocity on a highway when a bug hit the windshield and its dead body got stuck on the windscreen. Amar and Javed began discussing the situation. Amar suggested that the change in momentum of the bug is much greater than that of the bus. After all, argued Amar, there was no noticeable change in the velocity of the bus compared to the obvious change in the velocity of the bug. Javed opined that since the bus was moving with a larger velocity, so it exerted a larger force on the bug, as a result of which it died. Rita disagreed entirely, arguing that both the bug and bus experienced the same force and a change in their momentum. Who do you agree with? Support your answer.

Which has a higher value of momentum: $A$ bullet of mass $10 \, g$ moving with a velocity of $400 \, m s^{-1}$ or a cricket ball of mass $400 \, g$ thrown with a speed of $90 \, km h^{-1}$?

State and explain the law of inertia (or Newton's first law of motion).

Explain the following:
$(i)$ Why do the doors of a corridor train open or shut when the train starts or stops?
$(ii)$ Why is it necessary to run along with a moving bus in the same direction while alighting from it?
$(iii)$ Why does a player run for some distance before taking a long jump?
$(iv)$ Why does a person fall off the back of a stationary horse if the horse starts off suddenly?
$(v)$ Why is a neat hole formed in a glass pane if a bullet is fired at it from a close range?