Question

Total area under velocity-time graph give us the :

• A. acceleration
• B. velocity
• C. time
• D. displacement

Answer 1

The correct option is D displacement

The area covered between the velocity time graph and time axis gives the displacement and distance traveled by the body for a given time interval

Total distance$=\left|A_1\right|+\left|A_2\right|+\left|A_3\right|$

$=$ addition of modules of different area i.e., $s=\int \left|v\right|dt$

Total displacement$=A_1+A_2+A_3$

$=$ addition of modules of different area considering their sign i.e., $r=\int vdt$

Area above time axis is taken as positive, while area below time axis is taken as negative

Here $A_1$ and $A_2$ are area of triangle $1$ and $2$ respectively and $A_3$ is the area of trapezium