In a vleocity Vs time graph, the change in position of an object is given by
[tex]x_{1}-x_{2} =\int\limits^T_t {v} \, dt[/tex]
where the integral can be taken from the graph as
[tex]\int\limits^T_t {v} \, dt[/tex]=area between velocity curve and time axis from t to T
The displacement of an object is obtained by taking out the area of the velocity-time graph enclosed between the velocity curve and the time axis (x-axis).
What is a velocity-time graph?
The graphical representation of the speed and direction of an object covered over a specific period of time.
Consider an object that starts from the initial position and covered some distance upto the final position. Then as per the concept of a velocity-time graph, the change in position of an object is given as,
[tex]x_{2}-x_{1}=\int\limits^T_t {v} \, dt[/tex]
The integral part of the above expression can be written as,
[tex]x_{2}-x_{1}=\int\limits^T_t {v} \, dt =A[/tex]
Here, A is the area between the velocity curve and time axis (x-axis) taken from t to T. This area will provide the value of displacement of the object.
Thus, we can conclude that the displacement of an object is obtained by taking out the area of the velocity-time graph enclosed between the velocity curve and the time axis (x-axis).
Learn more about the velocity-time graph here:
https://brainly.com/question/3072589
