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Motion in one Dimension

Comparative Study Of Average Speed & Average Velocity

The average speed of a particle for a given interval of time is defined as the ratio of distance travelled to the time taken, while average velocity is defined as the ratio of displacement to time taken.
Average speed =
i.e. vav =
Average velocity =
i.e Note :(a) Average speed is a scalar, while average velocity is a vector both having same unit (m/s)
(b) Both have dimension [M0LT–1]
(c) For a given time interval average velocity is single valued, while average speed can have many values depending on path followed.
(d) If after motion body comes back to its initial position = 0 [as &Delta = 0], but vav > 0 and finite (as Δ s > 0)
(e) For a moving body average speed can never be negative or zero (unless t → ∞), while average velocity can be i.e.
Vav > 0 while > = or < 0
(f) In general average speed is not equal to magnitude of average velocity (as Δ s ≠ | Δ |). However it can be so if the motion is along a straight line without change in direction (as Δ s = | Δ |).
(g) If a graph is plotted between distance (or displacement) and time, the slope of chord during a given time interval gives average speed (or velocity)

IIT (Class X)