Question

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

Answer 1

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, $a=\frac{v}{t}$, 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 $A=\frac{1}{2}∆a\times ∆t$. …………………(1)

Again we know, $changeinvelocity=acceleration\times time$

Therefore, from equation (1),

$$\begin{gathered} \frac{1}{2}∆a\times ∆t=\frac{1}{2}∆v \\ or∆a\times ∆t=∆v.....................\left(2\right) \end{gathered}$$

Where $∆v$ refers to the change in velocity.

In integral form it is written as, $v={\int }_{t=0}^{t=t}adt$

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