the question is: How far does the object travel from *t* = 12.0 s to *t* = 14.0 s? 
 

To determine how far the object travels from \( t = 12.0 \) seconds to \( t = 14.0 \) seconds, we'll need to focus specifically on the portion of the velocity-time graph between these two times.

### Analysis:

1. **Velocity at \( t = 12 \) seconds**: From the graph, the velocity at \( t = 12 \) seconds is 20 m/s.
2. **Velocity at \( t = 14 \) seconds**: The graph shows that at \( t = 14 \) seconds, the velocity is 10 m/s. This is inferred by linearly interpolating between the values at \( t = 12 \) seconds and \( t = 16 \) seconds, where the velocity decreases from 20 m/s to 0 m/s.

### Approach:
Since we need the area under the curve from \( t = 12 \) to \( t = 14 \) seconds:

- The time interval \( \Delta t = 14 - 12 = 2 \) seconds.
- The velocities at \( t = 12 \) and \( t = 14 \) are 20 m/s and 10 m/s, respectively.
- The shape formed by these points is a trapezoid.

The area of the trapezoid will give us the distance traveled.

Let's calculate that now.The object travels **30 meters** from \( t = 12.0 \) seconds to \( t = 14.0 \) seconds.

Would you like further details or have any other questions about this calculation?

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Here are 5 related questions for further practice:
1. What would be the distance traveled from \( t = 14 \) seconds to \( t = 16 \) seconds?
2. How does the velocity change between \( t = 12 \) and \( t = 16 \) seconds, and what does that imply about the motion?
3. If the object continued to decelerate linearly, what would be its velocity at \( t = 15 \) seconds?
4. How far would the object travel if it maintained a constant velocity of 10 m/s from \( t = 14 \) seconds to \( t = 20 \) seconds?
5. What is the total distance traveled by the object from \( t = 0 \) seconds to \( t = 16 \) seconds?

**Tip:** When working with trapezoids on velocity-time graphs, you can quickly calculate the distance by using the formula for the area of a trapezoid. This method is particularly useful when dealing with non-uniform motion.

Learn how to calculate the distance traveled by an object from t = 12.0 s to t = 14.0 s using a velocity-time graph analysis. Understand the concept of areas under curves, specifically trapezoidal areas, in the context of kinematics. Suitable for high school students studying physics or applied mathematics.

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