A bullet fired into a fixed target loses half of tis velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

Let initial velocity of the bullet (at A)= u

After penetrating (AB) 3 cm its velocity becomes $\frac{u}{2}$

$From{v}^2=u^2-2as$

${\left(\frac{u}{2}\right)}^2=u^2-2a\left(3\right)$

$\Rightarrow 6a=\frac{3u^2}{4}\Rightarrow a=\frac{u^2}{8}$

Let it further penetrate through distance x and stops at point C.

$FordistanceBC,v=0,u=\frac{u}{2},s=x, a=\frac{u^2}{8}$

$From{v}^2=u^2-2as\Rightarrow 0={\left(\frac{u}{2}\right)}^2-2\left(\frac{u^2}{8}\right).x$

$\Rightarrow$x = 1 cm