1. Understand the Concepts

* Uniform deceleration: The bullet slows down at a constant rate.

* Work-Energy Theorem: The work done on an object equals its change in kinetic energy.

* Force and Work: Work done by a force is the force multiplied by the distance over which it acts.

2. Gather the Information

* Mass of bullet (m) = 2.5 g = 0.0025 kg

* Initial velocity (v₁) = 350 m/s

* Final velocity (v₂) = 0 m/s (comes to rest)

* Penetration distance (d) = 12 cm = 0.12 m

3. Calculate the Bullet's Initial Kinetic Energy

Kinetic energy (KE) = (1/2) * m * v²

KE = (1/2) * 0.0025 kg * (350 m/s)²

KE = 153.125 J

4. Calculate the Work Done on the Bullet

Since the bullet comes to rest, the change in kinetic energy is equal to its initial kinetic energy. Therefore, the work done on the bullet is:

Work (W) = -153.125 J (Negative because the force is opposing the motion)

5. Calculate the Force

Work (W) = Force (F) * Distance (d)

-153.125 J = F * 0.12 m

Force (F) = -153.125 J / 0.12 m

Force (F) = -1276.04 N

Therefore, the force exerted on the bullet to bring it to rest is approximately 1276.04 N. The negative sign indicates that the force is acting in the opposite direction of the bullet's motion.