The area under acceleration-time graph gives

Options

A. intial velocity
B. final velocity
C. change in velocity
D. distance travelled

Answer

To solve the question, "The area under the acceleration-time graph gives:", we can follow these steps:

### Step 1: Understand the acceleration-time graph
The acceleration-time graph represents how acceleration varies with time. The area under this graph is significant in kinematics.

### 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:
\[ a = \frac{\Delta v}{\Delta t} \]
where \( a \) is acceleration, \( \Delta v \) is the change in velocity, and \( \Delta t \) is the change in time.

### Step 3: Calculate the area under the graph
The area under the acceleration-time graph can be calculated as:
\[ \text{Area} = a \times \Delta t \]
This represents the product of acceleration and the time interval over which it acts.

### Step 4: Relate the area to change in velocity
From the definition of acceleration, we can rearrange the formula:
\[ \Delta v = a \times \Delta t \]
Thus, the area under the acceleration-time graph gives us the change in velocity (\( \Delta v \)) over the time interval \( \Delta t \).

### Step 5: Conclusion
Therefore, the area under the acceleration-time graph represents the change in velocity.

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

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