To determine the acceleration of the bullet, we can use the kinematic equation that relates the final velocity ($v$), initial velocity ($v_0$), distance traveled ($d$), and acceleration ($a$):

$v^2 = v_0^2 + 2ad$

Step-by-step:

1. Given:

   • Final velocity ($v$) = 521 m/s (the muzzle velocity of the bullet).
   • Initial velocity ($v_0$) = 0 m/s (since the bullet starts from rest).
   • Distance traveled ($d$) = 0.840 m.

2. Plug in the values into the equation:

$(521)^2 = (0)^2 + 2 \cdot a \cdot 0.840$

3. Simplify the equation:

$271,441 = 1.68a$

4. Solve for acceleration:

$a = \frac{271,441}{1.68} = 161,553.57 \, \text{m/s}^2$

Thus, the acceleration of the bullet is approximately:

$a = 1.62 \times 10^5 \, \text{m/s}^2$

Do you want more details or have any questions?

Here are 5 related questions for further practice:

1. What is the time taken for the bullet to travel through the barrel?
2. How would the acceleration change if the muzzle velocity was doubled?
3. What is the bullet's velocity after it has traveled halfway through the barrel?
4. How long would the barrel need to be if the bullet experienced an acceleration of $2.0 \times 10^5$ m/s²?
5. How would the problem change if there was a slight resistance inside the barrel?

Tip: When solving kinematics problems, identifying what you know and using the appropriate equation is key to finding the unknown variable!