Speed and Velocity

Objective: Compute total distance divided by elapsed time.

Average speed is total distance traveled divided by total elapsed time, v_avg, speed = d_total/Δt. It is a nonnegative scalar in ordinary motion descriptions. If a traveler covers 150 m in 30 s, average speed is 5 m/s, even if speed varies during the trip. Kilometers per hour and meters per second are both speed units; 1 m/s = 3.6 km/h. Average speed cannot in general be found by averaging two segment speeds without considering their times or distances. Time intervals must be positive and the measured distance must describe the same interval.

Objective: Compute displacement per time in a chosen direction.

Average velocity in one dimension is displacement divided by elapsed time, v_avg = Δx/Δt = (x_f − x_i)/Δt. Its sign describes the direction of net displacement along the chosen axis, while average speed is based on total distance. A round trip can have nonzero average speed and zero average velocity. If position changes from +2 m to −10 m over 4 s, average velocity is −3 m/s. The average does not specify velocity at every instant or guarantee constant motion. A change in reference frame can change numerical velocity, so state the frame.

Objective: Compare instantaneous readings with interval averages.

Instantaneous velocity is the rate of position change at a particular time and is represented by the local slope of a smooth position–time curve. Instantaneous speed is its magnitude. A speedometer estimates a near-instantaneous speed over a short sampling interval, whereas trip-average speed uses the entire route and time. A constant-speed object can change velocity when direction changes, as in turning along a curved path. Measurements over shorter intervals can approach an instantaneous description, but sensor sampling and noise limit estimates. Distinguish a single reading from an average over a stated interval.