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

(C) Momentum is defined as the product of the mass and velocity of an object. Its $SI$ unit is $kg\, m s^{-1}$.
$(b)$ Force is given by $F = m \times a$,where $a = (v - u) / t$.
$(i)$ For interval $O$ to $A$: $u = 0\, m s^{-1}$,$v = 40\, m s^{-1}$,$t = 2\, s$. Acceleration $a = (40 - 0) / 2 = 20\, m s^{-2}$. Force $F = 5\, kg \times 20\, m s^{-2} = 100\, N$.
$(ii)$ For interval $B$ to $C$: $u = 40\, m s^{-1}$,$v = 0\, m s^{-1}$,$t = (10 - 6) = 4\, s$. Acceleration $a = (0 - 40) / 4 = -10\, m s^{-2}$. Force $F = 5\, kg \times (-10\, m s^{-2}) = -50\, N$ (The negative sign indicates a retarding force).
$(c)$ Force required for $2\, kg$ mass: $F_1 = 2\, kg \times 5\, m s^{-2} = 10\, N$.
Force required for $4\, kg$ mass: $F_2 = 4\, kg \times 2\, m s^{-2} = 8\, N$.
Since $10\, N > 8\, N$,accelerating a $2\, kg$ mass at $5\, m s^{-2}$ requires a greater force.