The area under acceleration – time graph gives

• A. Change in acceleration.
• B. Change in velocity.
• C. Change in displacement.
• D. Change in deceleration.

The area under an acceleration-time graph represents a specific physical quantity, and in this case, it corresponds to the change in velocity. So, the correct answer to your question is B. Change in velocity. Let’s break this down to understand why that is the case.

Understanding Acceleration and Velocity

Acceleration is defined as the rate of change of velocity with respect to time. When you plot acceleration on the vertical axis and time on the horizontal axis, the area under the curve gives you valuable information about how velocity changes over that time period.

Why Area Represents Change in Velocity

To grasp this concept, consider the following:

• Acceleration: If an object is accelerating at a constant rate, the graph will be a straight line. The area under this line can be calculated as the area of a rectangle (if constant) or a triangle (if it varies).
• Integration Concept: Mathematically, the area under the acceleration-time graph can be thought of as the integral of acceleration with respect to time. This integral gives you the change in velocity, as integration is the process of summing up small changes over a period.

Example for Clarity

Imagine a car that starts from rest and accelerates uniformly at 2 m/s² for 5 seconds. The acceleration-time graph would be a horizontal line at 2 m/s² from 0 to 5 seconds. The area under this line can be calculated as:

• Area = base × height = time × acceleration = 5 s × 2 m/s² = 10 m/s.

This area indicates that the car's velocity increases by 10 m/s over that 5-second interval. Thus, the area under the acceleration-time graph directly correlates to the change in velocity.

Other Options Explained

Let’s briefly look at the other options to clarify why they are not correct:

• A. Change in acceleration: The area under the acceleration-time graph does not represent a change in acceleration; it represents how velocity changes.
• C. Change in displacement: Displacement is related to the area under a velocity-time graph, not an acceleration-time graph.
• D. Change in deceleration: While deceleration is a form of acceleration, the area under the graph still pertains to velocity changes, not deceleration specifically.

In summary, the area under an acceleration-time graph gives you the change in velocity, making option B the correct choice. Understanding these relationships is crucial in physics, as they help us analyze motion effectively.