Question

Given the velocity-time graph. How can it be used to find the displacement of the body in a given time:

• A. The net area of the colored region, under velocity-time graph
• B. The total area under velocity-time graph
• C. Slope of velocity-time graph
• D. None of the above

Answer 1

The correct option is A The net area of the colored region, under velocity-time graph

A velocity time graph gives displacement if we take areas under the graph with their respective signs and add them. The net area is the value of the displacement with sign. Sign represents the direction.
In the example shown, Area above the time axis will be positive and area below the time axis will be negative.
Area above the time axis, $D_1=\text{Area of brown square+Area of yellow triangle}=4m+2m=6m$
Area below the time axis, $D_2=\text{Area of red triangle(with a negative sign)}=-2m$
Displacement, $D=D_1+D_2=4m$