Question

Name the quantity which is measured by the area occupied by the velocity time graph for an object moving with certain uniform acceleration starting with some initial velocity u for time t . ​

Answer 1

DISTANCE the quantity which is measured by the area occupied by the velocity time graph for an object moving with certain uniform acceleration starting with some initial velocity u for time t . ​

PLEASE MARK AS BRAINLIEST

Answer 2

The area occupied by the velocity time graph for an object moving with certain uniform acceleration starting with some initial velocity "u" for time "t" measures the DISPLACEMENT of that object.

Proof:

As per the definition of velocity we can say that velocity is the instantaneous change of Displacement function with respect to time.

Let velocity be v , Displacement be s and time be t.

Mathematically , we can say :

$\boxed{ \sf{v = \dfrac{ds}{dt} }}$

Rearranging the Equation ;

$\sf{ = > ds = v \times dt}$

Integrating on both sides:

$\displaystyle\sf{ = > \int ds = \int v \times dt}$

For any velocity function , we can say that integration of (v dt) represents the area calculated under the velocity-time graph.

$\boxed{\displaystyle\sf{ \int ds = \int v \: dt= Area \:under\: Graph}}$