An object of mass $100 \,kg$ is accelerated uniformly from a velocity of $5 \,m \,s^{-1}$ to $8 \,m \,s^{-1}$ in $6 \,s$. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.

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.

$A$ 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.

Chetan's father wanted to buy a car. He visited many showrooms to find out the price and the specifications of various cars. In one of the showrooms,he was told by the salesman that their car had excellent brakes such that the car stops instantaneously. Chetan's father was impressed and decided to buy that car. In the evening,he discussed this with his family. Chetan told his father that such a car cannot be made and the salesman had lied to him. He told his father that he should not buy that car and,moreover,never from that showroom. He explained to his father why it is not possible. His father was convinced and promised to visit another showroom and be careful this time.
$(a)$ What might have been the explanation given by Chetan to convince his father?
$(b)$ What values do you see in Chetan?

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

Two similar vehicles are moving with the same velocity on roads,such that one of them is loaded and the other is empty. Which of the two vehicles will require a larger force to stop it? Give reasons.