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Illustration Position-Time Graph and Average Velocity as Slope

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: \(v = \Delta s / \Delta t\).