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 $90 \, km h^{-1}$?

It is required to increase the velocity of a scooter of mass $80 \ kg$ from $5 \ m s^{-1}$ to $25 \ m s^{-1}$ in $2 \ s$. Calculate the force required.

$A$ 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.

$A$ truck of mass $M$ is moved under a force $F$. If the truck is then loaded with an object equal to the mass of the truck and the driving force is halved,then how does the acceleration change?

$A$ goalkeeper in a game of football pulls his hands backwards after holding the ball shot at the goal. This enables the goalkeeper to

Using the second law of motion,derive the relation between force and acceleration. $A$ bullet of $10 \, g$ strikes a sandbag at a speed of $10^3 \, m \, s^{-1}$ and gets embedded after traveling $5 \, cm$. Calculate:
$(i)$ The resistive force exerted by the sand on the bullet.
$(ii)$ The time taken by the bullet to come to rest.