Average Velocity

Definition: Average Velocity is displacement over total time. Mathematically:
 

$$\bar{v} \equiv {\frac{\Delta x}{\Delta t}} \equiv {\frac{x_f - x_i}{t_f - t_i}} {\frac{displacement}{elapsed \,\,\,time}}$$ (1)

Note:

• the overbar is frequently used to denote an average quantity
• $\Delta$t is always > 0 so the sign of $\bar{v}$ depends only on the sign of $\Delta$x .

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

 

Figure 2.1: Graphical interpretation of velocity

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