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Average Velocity

Definition: Average Velocity is displacement over total time. Mathematically:
$\displaystyle\bar{v}$ $\displaystyle\equiv$ $\displaystyle{\frac{\Delta x}{\Delta t}}$ $\displaystyle\equiv$ $\displaystyle{\frac{x_f - x_i}{t_f - t_i}}$ = $\displaystyle{\frac{displacement}{elapsed \,\,\,time}}$      (1)

Graphical interpretation of velocity: Consider 1-d motion from point P (with coordinates xi , ti ) to point Q (at xf , tf ). We can plot the trajectory on a graph (see Figure 2.1).

Figure 2.1: Graphical interpretation of velocity
\epsfysize=8 cm

Then $\bar{v}$ from Eq.(2.1) is just the slope of the line joining P and Q.