Speed and Velocity

Objective: Calculate average speed from total path distance and elapsed time.

Average speed equals total distance divided by total elapsed time, v_avg,speed = d_total/Δt. Speed is nonnegative and expressed in distance-per-time units such as m/s. On a trip with different speeds, the arithmetic mean of speeds generally does not equal the average speed unless the time intervals are equal. Include pauses in elapsed time if the question asks for overall average speed.

Objective: Calculate signed average velocity from displacement and elapsed time.

Average velocity is displacement divided by elapsed time, v_avg = Δx/Δt. In one dimension the sign shows direction. A return trip has zero average velocity if its displacement is zero, regardless of distance traveled. Speed and the magnitude of velocity may differ for changing direction, and their averages require different numerators.

Objective: Convert speed units and distinguish instantaneous from trip averages.

Instantaneous speed describes the magnitude of velocity at an instant; average speed summarizes a finite time interval. Unit conversions must carry dimensions, for example 36 km/h × (1000 m/1 km) × (1 h/3600 s) = 10 m/s. A speedometer approximates instantaneous speed; it does not report the entire journey’s average. A negative velocity in a signed coordinate system can accompany increasing speed if acceleration points the same way.