Introduction:
In this scenario, a 60 kg bullet is fired through a stack of fibreboard sheets, which are 200 mm thick. The bullet approaches the stack with a velocity of 600 m/s. We need to determine the average retarding force offered to the bullet during its passage through the stack.

Calculation of Deceleration:
To calculate the average retarding force, we first need to find the deceleration experienced by the bullet. We can use the equation of motion:

v^2 = u^2 + 2as

Where:
v = final velocity (0 m/s, as the bullet comes to rest)
u = initial velocity (600 m/s)
a = acceleration (deceleration in this case)
s = displacement (200 mm = 0.2 m)

Rearranging the equation, we have:

a = (v^2 - u^2) / 2s

Plugging in the values, we get:

a = (0^2 - 600^2) / (2 * 0.2)

Simplifying further, we find:

a = -900,000 m/s^2

Explanation of Negative Sign:
The negative sign indicates that the acceleration is in the opposite direction of the bullet's initial velocity. Since the bullet is moving forward, the deceleration acts in the opposite direction to slow it down.

Calculation of Retarding Force:
Now, we can calculate the average retarding force using Newton's second law of motion:

F = ma

Where:
F = force applied (retarding force)
m = mass of the bullet (60 kg)
a = acceleration (from previous calculations)

Plugging in the values, we find:

F = 60 kg * (-900,000 m/s^2)

Simplifying further, we get:

F = -54,000,000 N

Explanation of Negative Sign:
The negative sign indicates that the retarding force acts in the opposite direction of the bullet's motion. It opposes the forward velocity and slows down the bullet.

Conclusion:
The average retarding force offered to the bullet as it passes through the stack of fibreboard sheets is -54,000,000 N. This force acts in the opposite direction of the bullet's motion and causes it to decelerate.

first formula is V^2=2*d*a