The question asks how to calculate the displacement of a bottle after one second, given the average velocity. Let's review the provided options:

1. $\text{avg } v = \frac{d}{t}$: This equation relates average velocity ($v$) to displacement ($d$) and time ($t$). Rearranging this equation as $d = v \cdot t$, it could be used if the average velocity is known.

2. $d = v_0 t + \frac{1}{2} a t^2$: This equation is the standard kinematic equation for displacement when initial velocity ($v_0$) and acceleration ($a$) are known. However, this formula isn't directly based on average velocity.

3. $a = \frac{v_f - v_0}{t}$: This is the formula for acceleration ($a$) when the final velocity ($v_f$) and initial velocity ($v_0$) are known, along with the time ($t$). It doesn’t help directly with displacement.

Given that you are working with average velocity, the most appropriate formula would be $\text{avg } v = \frac{d}{t}$, as you can directly solve for displacement using $d = \text{avg } v \cdot t$.

Do you need further details or explanations? Here are some related questions to explore:

1. What is the definition of average velocity?
2. How is average velocity different from instantaneous velocity?
3. How would you calculate displacement if acceleration were constant?
4. Can you derive displacement from velocity if the velocity is not constant?
5. What role does time play in determining displacement?

Tip: To calculate displacement using average velocity, remember that the formula assumes constant velocity unless additional information, like acceleration, is given.