The quantitative definition of force is given by

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?

$(a)$ Define momentum and mention its $SI$ unit.
$(b)$ From the velocity-time graph shown in the figure for a body of mass $5\, kg$,find the force on the body from:
$(i)$ $O$ to $A$ and $(ii)$ $B$ to $C$.
$(c)$ Which would require a greater force: accelerating a $2\, kg$ mass at $5\, m s^{-2}$ or a $4\, kg$ mass at $2\, m s^{-2}$?

Define $(i)$ force $(ii)$ dyne $(iii)$ newton.

$(a)$ $(i)$ 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.

State whether the following statement is true or false:
Impulse represents the rate of change of momentum of a body.