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The problem requires finding the best equation to solve for the distance (\(\Delta x\)) a turtle travels, given the following:

- Acceleration (\(a\)) = 0.126 m/s²
- Initial velocity (\(v_i\)) = 0.500 m/s
- Final velocity (\(v_f\)) = 0.899 m/s

From the provided options, we need to choose the one that allows us to calculate \(\Delta x\) without requiring time, as time is not provided.

### Reviewing the formulas:

A) \( v_f^2 = v_i^2 + 2a\Delta x \)  
This equation does not require time, and we can solve for \(\Delta x\).

B) \( \Delta x = \frac{1}{2}(v_f + v_i)t \)  
This equation requires time, which we don't have.

C) \( v_f = v_i + at \)  
This equation solves for velocity, not distance.

D) \( \Delta x = v_ft - \frac{1}{2}at^2 \)  
This requires time as well.

E) \( \Delta x = v_it + \frac{1}{2}at^2 \)  
This also requires time.

### Correct Answer:
The best equation is **A**: \( v_f^2 = v_i^2 + 2a\Delta x \). This can be solved directly for \(\Delta x\).

Would you like a detailed solution using this equation?

Here are some related questions:
1. How do you rearrange formula A to solve for \(\Delta x\)?
2. What would be the turtle's time of travel if it were provided?
3. Can formula A be used if acceleration was negative? How?
4. What is the importance of each term in equation A for this scenario?
5. How does the formula for displacement change if velocity remains constant?

**Tip:** Always check what variables are provided and which are missing before selecting the equation!

A turtle accelerates at 0.126 m/s² with an initial velocity of 0.500 m/s and a final velocity of 0.899 m/s. How far did the turtle travel?

Learn how to calculate the distance traveled by an accelerating object using the kinematic equation v_f^2 = v_i^2 + 2aΔx. In this example, a turtle accelerates from 0.500 m/s to 0.899 m/s with an acceleration of 0.126 m/s². Ideal for high school students in Grades 10-12.

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