Consider the following velocity over time graphs. Order them by displacement during the time a line is shown on the graph. Order from least to greatest. 50----------||²||||| 50 DESTRU

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**Ordering Velocity over Time Graphs by Displacement**

Consider the following velocity over time graphs. Order them by displacement during the time a line is shown on the graph. Order from least to greatest. 

### Graph Descriptions:

1. **Graph on the Left:**
   - **Line A:**
     - Starts at (0 s, 0 m/s) and ends at (25 s, 30 m/s).
   - **Line B:**
     - Starts at (0 s, 40 m/s) and ends at (25 s, 50 m/s).

2. **Graph on the Right:**
   - **Line C:**
     - Starts at (0 s, 20 m/s) and remains constant until (25 s, 20 m/s).
   - **Line D:**
     - Starts at (0 s, 40 m/s) and remains constant until (25 s, 40 m/s).

### Analysis:

To find the displacement, calculate the area under each line:
1. **Line A (Left Graph):**
   - A triangle with base = 25 s and height = 30 m/s. 
   - Area = 1/2 * base * height = 1/2 * 25 s * 30 m/s = 375 m.

2. **Line B (Left Graph):**
   - Trapezoid with the following bases and height:
     - Base 1: 40 m/s
     - Base 2: 50 m/s
     - Height: 25 s
   - Area = 1/2 * (Base 1 + Base 2) * height = 1/2 * (40 m/s + 50 m/s) * 25 s = 1/2 * 90 m/s * 25 s = 1125 m.

3. **Line C (Right Graph):**
   - A rectangle with base = 25 s and height = 20 m/s. 
   - Area = base * height = 25 s * 20 m/s = 500 m.

4. **Line D (Right Graph):**
   - A rectangle with base = 25 s and height = 40 m/s. 
   - Area = base * height = 25 s * 40 m/s = 1000 m.

### Order Lines by Displacement (Least to Greatest):

- A
- C
Transcribed Image Text:**Ordering Velocity over Time Graphs by Displacement** Consider the following velocity over time graphs. Order them by displacement during the time a line is shown on the graph. Order from least to greatest. ### Graph Descriptions: 1. **Graph on the Left:** - **Line A:** - Starts at (0 s, 0 m/s) and ends at (25 s, 30 m/s). - **Line B:** - Starts at (0 s, 40 m/s) and ends at (25 s, 50 m/s). 2. **Graph on the Right:** - **Line C:** - Starts at (0 s, 20 m/s) and remains constant until (25 s, 20 m/s). - **Line D:** - Starts at (0 s, 40 m/s) and remains constant until (25 s, 40 m/s). ### Analysis: To find the displacement, calculate the area under each line: 1. **Line A (Left Graph):** - A triangle with base = 25 s and height = 30 m/s. - Area = 1/2 * base * height = 1/2 * 25 s * 30 m/s = 375 m. 2. **Line B (Left Graph):** - Trapezoid with the following bases and height: - Base 1: 40 m/s - Base 2: 50 m/s - Height: 25 s - Area = 1/2 * (Base 1 + Base 2) * height = 1/2 * (40 m/s + 50 m/s) * 25 s = 1/2 * 90 m/s * 25 s = 1125 m. 3. **Line C (Right Graph):** - A rectangle with base = 25 s and height = 20 m/s. - Area = base * height = 25 s * 20 m/s = 500 m. 4. **Line D (Right Graph):** - A rectangle with base = 25 s and height = 40 m/s. - Area = base * height = 25 s * 40 m/s = 1000 m. ### Order Lines by Displacement (Least to Greatest): - A - C
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