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Motion in One Dimension – Velocity

Velocity

It is defined as rate of change of displacement and it is a vector quantity

(i) Instantaneous Velocity :

It is defined as the velocity at some particular instant. Instantaneous velocity is also called simply velocity.

Instantaneous velocity = \displaystyle \underset{\Delta t\to 0}{\mathop{\lim }}\,\frac{\Delta \overset{\to }{\mathop{r}}\,}{\Delta t} = \displaystyle \frac{d\overset{\to }{\mathop{r}}\,}{dt}

(ii)Average Velocity :

Average velocity = \displaystyle \frac{Total\,\,\,\,displacement}{Total\,\,\,\,time}

(iii)Uniform Velocity :

A particle is said to have uniform velocity, if magnitude as well as  direction of its velocity remains same and this is possible only when the  particles moves in same straight line without reversing its direction.

Special Note :

(a) If a particle moves a distance at speed v1 and  comes back with speed v2, then 

Average speed

vav   = \displaystyle \frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}

& average velocity= 0 [as displacement = 0]

(b) If a particle moves for two equal time-intervals with speed v1 and v2 respectively then average speed   

vav = \displaystyle \frac{{{v}_{1}}+{{v}_{2}}}{2}

(c) Since |displacement| <= distance,

hence |average velocity| <= average speed i.e.

Magnitude of average velocity is always less than or equal to average speed for the same interval of time.

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