Velocity First, then Speed, Average-Velocity, and Average-Speed

We present a pedagogical approach to introducing velocity first, emphasizing its distinction from speed, average-velocity, and average-speed. Velocity is defined as the slope of the tangent line on a position-vs-time graph, modeled by a left hand riding the position graph. Speed is defined as the magnitude of velocity. Average-velocity is then defined as a time-weighted average of velocities and is interpreted as the steady velocity needed to make the trip with the same start and end positions in the same elapsed time. Average-speed is defined analogously for a trip with the same endpoints and same intermediate turning positions. We provide a piecewise constant-velocity example, accompanied by an interactive Desmos visualization.