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To determine the displacement between 0 and 4 seconds from the given velocity-time graph, we need to find the area under the graph between those two time points. Displacement is the area under the velocity-time curve.

### Step-by-step process:

1. **From 0 to 2 seconds:**
   - The velocity starts at \( -12 \, \text{m/s} \) and linearly increases to \( -6 \, \text{m/s} \).
   - The shape of the graph in this section forms a trapezoid.
   - The area of the trapezoid can be calculated as:
   \[
   \text{Area}_1 = \frac{1}{2} \times (b_1 + b_2) \times h
   \]
   Where:
   - \( b_1 = -12 \, \text{m/s} \) (initial velocity),
   - \( b_2 = -6 \, \text{m/s} \) (final velocity at \( t = 2 \) seconds),
   - \( h = 2 \, \text{seconds} \) (time duration).
   \[
   \text{Area}_1 = \frac{1}{2} \times (-12 + (-6)) \times 2 = \frac{1}{2} \times (-18) \times 2 = -18 \, \text{m}.
   \]

2. **From 2 to 4 seconds:**
   - The velocity remains constant at \( -6 \, \text{m/s} \), forming a rectangle.
   - The area of the rectangle is:
   \[
   \text{Area}_2 = v \times t = -6 \, \text{m/s} \times 2 \, \text{seconds} = -12 \, \text{m}.
   \]

### Total Displacement:
\[
\text{Total Displacement} = \text{Area}_1 + \text{Area}_2 = -18 \, \text{m} + (-12 \, \text{m}) = -30 \, \text{m}.
\]

Thus, the displacement between 0 and 4 seconds is **-30 meters**, which corresponds to option **E**.

Would you like more details on this solution, or any clarifications?

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Here are some related questions for further practice:

1. How would the displacement change if the velocity remained constant at \( -12 \, \text{m/s} \) for the entire 4 seconds?
2. How do you calculate displacement from a velocity-time graph if the curve is non-linear?
3. What does negative displacement indicate about the motion of the car?
4. How can you find the acceleration from a velocity-time graph?
5. What is the significance of the area under a velocity-time graph in physics?

**Tip:** Always pay attention to the shape of the graph (e.g., trapezoid, rectangle) when calculating areas for displacement.

What is the displacement in the x direction between 0 and 4 seconds as measured by a velocity-time graph?

Learn how to calculate displacement from a velocity-time graph. This problem involves analyzing the area under the graph for a trapezoid and rectangle, applying kinematic formulas to calculate the displacement between 0 and 4 seconds. Suitable for students in Grades 9-12.

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