https://file.aiquickdraw.com/mathbot/file/1724463393769erd8ordy.jpg

Hint: What does the area under the curve give?

The graph provided shows a velocity-time graph, which is a plot of velocity (in meters per second) against time (in seconds).

### Interpretation:
In a velocity-time graph, the area under the curve represents the displacement (distance traveled) of the object. To solve the problem, we need to calculate the area under the curve from \( t = 2 \) s to \( t = 14 \) s.

### Steps:
1. **Identify the Shape:** The area under the curve from \( t = 2 \) s to \( t = 14 \) s consists of geometric shapes (typically rectangles, triangles, or trapezoids).

2. **Calculate the Area of Each Shape:** 
   - From \( t = 2 \) s to \( t = 8 \) s, the area forms a trapezoid.
   - From \( t = 8 \) s to \( t = 12 \) s, the area forms a triangle.
   - From \( t = 12 \) s to \( t = 14 \) s, the area forms another trapezoid.

3. **Sum the Areas:** Add the areas of the trapezoid, triangle, and the second trapezoid to find the total displacement.

#### Do you want to proceed with these steps, or would you like a more detailed breakdown for each part? 

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### Relative Questions:
1. What are the units for displacement in a velocity-time graph?
2. How do you calculate the area of a trapezoid?
3. Why does the area under the velocity-time graph represent displacement?
4. What is the significance of the slope in a velocity-time graph?
5. How would the graph differ if it represented acceleration instead of velocity?

### Tip:
When dealing with velocity-time graphs, always remember that the slope gives you acceleration, and the area under the curve gives you displacement.

Explore how to find displacement using the area under the curve in a velocity-time graph. This detailed explanation covers identifying shapes like trapezoids and triangles, calculating their areas, and summing them up to find total displacement. Suitable for students studying calculus and velocity-time graphs.

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