The area under acceleration-time graph gives

Options

A. Distance travelled
B. Change in acceleration
C. Force acting
D. Change in velocity

Answer

To solve the question regarding what the area under the acceleration-time graph represents, we can follow these steps:

### Step 1: Understand the Axes of the Graph
The acceleration-time graph has acceleration (a) on the y-axis and time (t) on the x-axis.

### Step 2: Recall the Relationship Between Acceleration and Velocity
Acceleration is defined as the rate of change of velocity with respect to time. Mathematically, this can be expressed as:
\[ a = \frac{dv}{dt} \]
where \( v \) is velocity.

### Step 3: Determine the Area Under the Graph
The area under the acceleration-time graph can be calculated using the formula for the area of a shape (like rectangles or triangles) depending on the graph's shape. This area represents the change in velocity over the time interval considered.

### Step 4: Relate Change in Velocity to Final and Initial Velocity
From the area under the acceleration-time graph, we can express the change in velocity (\( \Delta v \)):
\[ \Delta v = v_f - v_i = \text{Area} \]
where \( v_f \) is the final velocity and \( v_i \) is the initial velocity.

### Step 5: Conclusion
Thus, the area under the acceleration-time graph gives the change in velocity of the object over the time interval considered.

### Final Answer
The area under the acceleration-time graph gives the change in velocity.

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