This question involves the motion of a bullet passing through a board, which requires applying the equations of motion under constant acceleration.

Given data:

• Distance traveled by the bullet through the board (d): 14 cm = 0.14 m
• Initial velocity (u): 220 m/s (the bullet enters the board with this speed)
• Final velocity (v): 0 m/s (we assume the bullet comes to rest after passing through the board)
• Acceleration (a): We need to calculate this.

We will use the following equation of motion:

$v^2 = u^2 + 2ad$

Where:

• $v$ = final velocity = 0 m/s
• $u$ = initial velocity = 220 m/s
• $d$ = distance = 0.14 m
• $a$ = acceleration (the unknown)

Rearranging to solve for acceleration $a$:

$a = \frac{v^2 - u^2}{2d}$

Substitute the known values:

$a = \frac{(0)^2 - (220)^2}{2(0.14)}$

$a = \frac{-48400}{0.28}$

$a \approx -1.73 \times 10^5 \, \text{m/s}^2$

So, the acceleration of the bullet is approximately $-1.73 \times 10^5 \, \text{m/s}^2$, which is negative because the bullet is decelerating as it passes through the board.

Would you like more details or have any further questions about this solution?

Here are some related questions you may find interesting:

1. How would the acceleration change if the bullet traveled through a thicker board?
2. What effect would a higher initial velocity have on the bullet's deceleration?
3. How does the deceleration in this case compare to that in free fall?
4. What other methods can be used to determine the acceleration of an object?
5. How could you calculate the time taken for the bullet to pass through the board?

Tip: Always ensure that units are consistent throughout the problem (e.g., meters and seconds) to avoid errors in calculations.