1. Speed: Speed is a scalar quantity. This is a distance traveled by an object per unit time. Speed does not depend on the direction but on the total length in any direction. The unit of speed is $m/s$.
If $d$ is the distance traveled in time $t$, then speed $(S)$ = $\frac{distance\; (d)}{time \;(t)}$.
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(i) Average Speed: total distance traveled by the object in any direction in one second. It is defined as the rate of change of distance of the object from the fixed point. It's unit is $m/s$.
Let $S$ be the total distance traveled by the object in time interval $t_1$ to $t_2$.
i.e. $S_{av}$ = $\frac{S}{t_2 - t_1}$ (∵ ${t_2 - t_1}$ = $ \Delta t$).
(ii) Instantaneous Speed: The speed of the object at a particular moment.It's unit is $m/s$. Let $\Delta S$ be the very small distance travelled by an object in a very short time interval $\Delta t$, approaches to zero.
i.e. Instantaneous Speed ($S$) = $\lim_{\Delta t\rightarrow 0}$ = $\frac{\Delta S}{\Delta t}$
2. Velocity: Velocity is a Vector quantity. This is a Displacement of the body per unit time. Velocity depends on the direction of motion. The unit of velocity is $m/s$.
Let $D$ be the displacement traveled in time $t$, then velocity $(V)$ = $\frac{D}{t}$. [i.e. $\frac{Distance\; + \;Direction}{time}$].
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(i) Average Velocity: It is defined as the ratio of its total displacement to the total time interval in which the displacement occurs.
$S_{av}$ = $\frac{S_2 - S_1}{t_2 - t_1}$ = $\frac{\Delta S}{\Delta t}$.
(∵ $ \Delta S$ = total displacement and $ \Delta t$ = total time)
(ii) Instantaneous Velocity: The velocity of an object at any given instant of time at particular point of its path is called instantaneous velocity.
Instantaneous Velocity($S$) = $\lim_{\Delta t\rightarrow 0}$ = $\frac{\Delta S}{\Delta t}$
Uniform and Non-Uniform Velocity:
Uniform Velocity: If a body travels equal distances in equal intervals of time.
Non-Uniform Velocity: If an object does not travel equal distances in equal intervals of time or the direction of motion changes, the body is said to be in non-uniform (Variable) velocity.
