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Question

On acceleration-time graph the area under the curve equals the:


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Solution

Step 1: Acceleration

  1. Acceleration is the time rate of change in velocity. It is a vector quantity.
  2. The acceleration is defined by the form, a=vt, where, v is the velocity of the body and t is the time.

Step 2: Diagram

Step 3: Finding the area under the acceleration-time graph

Let us consider the triangle on the above graph.

The base of the triangle indicates the time interval, suppose it is t and the height of the triangle indicates the change in acceleration, suppose it is a.

Now, the area of the triangle is A=12a×t. …………………(1)

Again we know, changeinvelocity=acceleration×time

Therefore, from equation (1),

12a×t=12vora×t=v.....................(2)

Where v refers to the change in velocity.

In integral form it is written as, v=t=0t=tadt

Therefore, on the acceleration-time graph, the area under the curve at a particular time interval will give the rate of change in velocity.


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