Two friends on roller-skates are standing $5\, m$ apart facing each other. One of them throws a ball of $2\, kg$ towards the other,who catches it. How will this activity affect the position of the two? Explain your answer.

$(a)$ 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 $2\, m s^{-2}$?

$A$ man is at rest in the middle of a pond on perfectly smooth ice. He can get himself to the shore by making use of Newton's:

State whether the following statement is true or false:
Force may or may not produce any motion in a body.

$A$ 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?

$(a)$ If the mass of a body is doubled, what happens to its acceleration when acted upon by the same force? Justify your answer.
$(b)$ It is easier to stop a tennis ball than a cricket ball moving with the same speed. Why?
$(c)$ A girl of mass $40 \, kg$ jumps with a horizontal velocity of $5 \, m s^{-1}$ onto a stationary cart with frictionless wheels. The mass of the cart is $10 \, kg$. Find her velocity as the cart starts moving. Assume that there is no external unbalanced force working in the horizontal direction.