Acceleration versus time graph for four objects are shown below. All axes have the same scale. Which object had the greatest change in velocity during the interval ?

Options

A. .
B. .
C. .
D. .

Explanation

To determine which object had the greatest change in velocity during the interval from the acceleration versus time graphs, we can follow these steps:

### Step 1: Understand the relationship between acceleration and change in velocity
The change in velocity (\( \Delta v \)) can be calculated using the formula:
\[ \Delta v = \int a \, dt \]
This means that the change in velocity is equal to the area under the acceleration versus time graph.

### Step 2: Identify the area under each graph
To find the change in velocity for each object, we need to calculate the area under the acceleration-time graph for each object. The area can be calculated by identifying the shapes formed under the curve (rectangles, triangles, etc.) and applying the appropriate area formulas.

### Step 3: Calculate the area for each object
1. **Object A**: Calculate the area under the curve for Object A. If it forms a triangle or rectangle, use the respective area formula.
2. **Object B**: Calculate the area under the curve for Object B.
3. **Object C**: Calculate the area under the curve for Object C.
4. **Object D**: Calculate the area under the curve for Object D.

### Step 4: Compare the areas
Once you have calculated the areas for all four objects, compare them to determine which one is the largest. The object with the largest area under the curve will have the greatest change in velocity.

### Step 5: Conclusion
The object with the greatest area under the acceleration versus time graph corresponds to the greatest change in velocity. Based on the analysis, conclude which object had the greatest change in velocity.