By definition, we have that the displacement of the object is given by:
\(r = \int\limits^t_0 {v} \, dt\)
Where,
v: object velocity
dt: time differential
Therefore, since the integral of a function is the area under the curve of the function, then in a graph of velocity vs time, we have that the displacement is:
The area under the curve of the velocity vs. time graph.
Answer:
to calculate the displacement of the object we have to calculate:
The area under the curve of the velocity vs. time graph.
