Average Velocity and Average Speed

Average Velocity

The rate of change of displacement of an object with respect to time. It is a vector quantity.

Average Speed

The rate of change of total distance traveled by an object with respect to time. It is a scalar quantity.

Displacement

The shortest distance between the initial and final positions of an object, with direction. It is a vector quantity.

Distance

The total length of the path traveled by an object. It is a scalar quantity.

Average Velocity

$\vec{x}_f$ is final position, $\vec{x}_i$ is initial position, $\Δ t$ is time interval.

\vec{v}_{avg} = \frac{\Δ \vec{x}}{\Δ t} = \frac{\vec{x}_f - \vec{x}_i}{t_f - t_i}

Average Speed

Total distance is the length of the path traveled.

v_avg = \frac{\text{Total Distance}}{\Δ t} = \frac{\text{Total Path Length}}{t_f - t_i}