Motion in Straight Line

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• Summary

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

$Ins\tan \tan eous speed v = \underset{∆t\to 0}{lim} \frac{∆s}{∆t} =\frac{ds}{dt}$

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

$Ins\tan \tan eous velocity \overrightarrow{v} = \underset{t\to 0}{lim}\frac{∆{\displaystyle \overrightarrow{r}}}{∆t} = \frac{\overrightarrow{dr}}{dt}$

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.