Instantaneous Velocity And Speed | Motion In A Straight Line | Notes | Summary - Zigya

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Motion in Straight Line

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Instantaneous Velocity And Speed

Instantaneous speed: It is the speed of a particle at a particular instant.
The instantaneous speed is the average speed for an infinitesimally small time interval(i.e., ∆t -> 0 ). Thus

Instantaneous speed v = limt0 st =dsdt

Instantaneous velocity: Instantaneous velocity is defined as the rate of change of position vector of particles with time at a certain instant of time.

Instantaneous velocity v = limt0rt = drdt

Comparison between average speed and average velocity

(a) Average speed is scalar while average velocity is a vector both having same units (m/s) and dimensions [LT-1]

(b) Average speed or velocity depends on time interval over which it is defined.

(c) For a given time interval average velocity is single-valued while average speed can have many values depending on the path followed.

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