How is displacement found from a velocity time graph?
Area under the velocity time graph
The velocity time graph has two axis - the velocity along the y-axis and time along the x-axis. both velocity as well as time are physical quantities.
Whenever we have physical quantities along the axis (velocity-time in this instance) find the product or ratio of the two quantities - if they correspond to another derived quantity we use the identity to find it.
e.g. in a velocity-time graph dividing velocity by time is acceleration therefore
Similarly in a velocity-time graph multiplying velocity by time is distance therefore
We do not say displacement as the product does not account for direction.