A bullet fired into a fixed target losses half of its velocity after penetrating 3cm. Then  further distance it will penetrate before coming to rest, assuming that it faces constant resistance to motion?

According to work-energy theorem
Total work done = Change in kinetic energy
Case-I  $-F\times 3=\frac{1}{2}m{\left(\frac{v_0}{2}\right)}^2-\frac{1}{2}m{v}_0^2$

Where F is resistive force and $v_0$  is initial speed

Case-II Let, the further distance travelled by the bullet before coming to rest be s

$\therefore -F(3+s)=K_{ƒ}-K_{ƒ}=-\frac{1}{2}m{v}_0^2;s=1cm$