Question

The area under acceleration time graph gives
(A). change in acceleration
(B). change in velocity
(C). change in displacement
(D). change in deceleration

Answer 1

Hint: The acceleration is the rate of change of velocity. The acceleration time graph gives the relation of how acceleration changes with time. It can be positive or negative deceleration. Time is the independent quantity while acceleration is the dependent quantity.

Formula used:
$a={\displaystyle \frac{dv}{dt}}$

Complete step-by-step answer:
Acceleration can be defined as the change in velocity per second. Its SI unit is $m{s}^{-2}$. A body is under acceleration when an external force is acting on it. Therefore,
$a={\displaystyle \frac{dv}{dt}}$ - (1)
Here, $a$ is the acceleration
$dv$ is the change in velocity
$dt$ is the change in time
The area of the acceleration time graph is given by-
$A=a\times t$
$\Rightarrow A=a\mathrm{\Delta }t$ - (2)
Therefore, from eq (1) and eq (2), we can say that
$\begin{array}{rl}& a\times dt=dv\\ & \Rightarrow a\mathrm{\Delta }t=\mathrm{\Delta }v\\ & \therefore A=\mathrm{\Delta }v\end{array}$
From the above, equation the area under acceleration time graph is equal to change in velocity
Therefore, the area covered under the acceleration time graph is equal to the magnitude of change in velocity. Hence, the correct option is (B).

So, the correct answer is “Option B”.

Additional Information: The acceleration, velocity and displacement are used to describe the motion of an object in one dimension. For motion in two dimensions, these terms are individually described for both the axes used. The resultant velocity, acceleration is calculated by using vector laws of addition or subtraction.

Note: The acceleration is one of the factors along with mass which determines the magnitude of force. When the acceleration of a body is constant, the force acting on it is constant. If acceleration is zero, no force is acting on a body, this relation between force and acceleration is given by Newton’s second law.