Question

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

Answer 1

The bullet's kinetic energy just as it hits the target is (1/2) (mass) (speed in air)².

After 3 cm, its speed is reduced to half, so its KE is (1/2) (mass) (1/2 speed in air)².
That's only 1/4 of its original KE. It lost 3/4 of its energy so far.

As it tears through the target, the force against it is constant. So the energy
taken away from it is (whatever the force is) x (the distance it travels).

It lost 3/4 of its energy in 3 cm. So it's losing 1/4 of its energy each centimeter,
and it has only 1 more cm to go before it stops completely.