The definition of speed and the graphical analysis allows to find the result for the question of the meaning of the area under the curve is:
Velocity is defined as the variation of position with respect to time.
[tex]v = \frac{dx}{dt}[/tex]
Where v is the velocity, x the displacement and t the time.
If we make a graph of speed versus time, see attached, where we have a diagram of the process.
The expression of the velocity for the case of zero acceleration is
[tex]v = \frac{\Delta x}{\Delta t }[/tex]
Δx = v Δt
They indicate that the shaded section is under the curve, therefore it is
Area = Δv Δt
When comparing the two expressions they are equivalent, therefore the area is equal to the distance traveled.
In conclusion, using the definition of velocity and graphical analysis we can find the result for the question of the meaning of the area under the curve is:
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