# Illustration Position-Time Graph and Average Velocity as Slope

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Position-time graph (x-t graph) with an example of a trajectory $$s(t)$$. The graph indicates the position $$x$$ of the body at a given time $$t$$.

Here $$x_1$$ is the position of the body at time $$t_1$$ and $$x_2$$ is the position of the body at time $$t_2$$. The distance traveled between $$x_2$$ and $$x_1$$ is: $$\Delta s = x_2 - x_1$$. And the time needed for it is: $$\Delta t = t_2 - t_1$$. The average velocity $$v$$ that this body has on the distance $$\Delta s$$ is given by: $$v = \Delta s / \Delta t$$.