What does the area under the velocity-time graph represent?

Concept:

• Displacement: The change in position is called displacement. It is the shortest distance that can be traveled between two points.
• Velocity: The rate of displacement is called velocity. It is a vector quantity. like displacement.

\(\overrightarrow{v} = \frac{\overrightarrow{ds}}{dt}\)

s is displacement, t is time.

• Acceleration: The rate of change of velocity is called acceleration.

\(\overrightarrow{a} = \frac{\overrightarrow{dv}}{dt}\)

Explanation:

The velocity-time graph is given below.

The area under curve will be (Trapezium Area)

\(A = \frac{1}{2} (v_2 + v_1)(t_2-t_1)\)

Here we can see we are multiplying velocity with time, which will give displacement. 

So, the Area under the velocity-time graph gives the displacement.

Important Points

• Area under acceleration time graph gives velocity.
• The slope of the velocity-time graph gives acceleration.
• The slope of the distance-time graph gives speed.