$A$ woman throws an object of mass $500\,g$ with a speed of $25\,ms^{-1}$.
$(a)$ What is the impulse imparted to the object?
$(b)$ If the object hits a wall and rebounds with half the original speed,what is the change in momentum of the object?

(N/A) Mass of the object $(m) = 500\,g = 0.5\,kg$.
Speed of the object $(v) = 25\,ms^{-1}$.
$(a)$ Impulse imparted to the object is equal to the change in momentum.
Impulse $= m(v - u) = 0.5\,kg \times (25\,ms^{-1} - 0\,ms^{-1}) = 12.5\,N\,s$.
$(b)$ The object rebounds with half the original speed,so the final velocity $(v') = -12.5\,ms^{-1}$ (taking the initial direction as positive).
Change in momentum $= m(v' - v) = 0.5\,kg \times (-12.5\,ms^{-1} - 25\,ms^{-1}) = 0.5 \times (-37.5) = -18.75\,kg\,ms^{-1}$ (or $-18.75\,N\,s$).