Mass of the object $(m)=500 \mathrm{~g}=0.5 \mathrm{~kg}$

Speed of the object $(v)=25 \mathrm{~m} / \mathrm{s}$

$(a)$ Impulse imparted to the object = change in momentum

$=m v-m u$

$=m(v-u)$

$=0.5(25-0)=12.5 \mathrm{~N} \mathrm{~s}$

$(b)$ Half of initial velocity is,

$\quad=-\frac{25}{2} \mathrm{~m} / \mathrm{s}$

$v^{\prime}=-12.5 \mathrm{~m} / \mathrm{s}$

$\therefore \text { Change in momentum } =m\left(v^{\prime}-v\right)$

$=0.5(-12.5-25)$

$=-18.75 \mathrm{~N} \mathrm{~s}$