If the time taken to bring a ball to rest from a certain velocity $v$ is reduced to half,what will be the changes in values of
$(a)$ Initial and final momentum.
$(b)$ Change of momentum.
$(c)$ Rate of change of momentum.

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?

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.

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.

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

What would happen if a fielder stops a fast-moving ball suddenly? Justify your answer.