The instantaneous velocity is defined as the velocity of an object at a particular instant of time. The instantaneous speed is defined as the limiting value of the average speed. Thus when time interval is very small, the magnitude of the displacement is effectively equal to the distance travelled by the object in the same small interval of time.Thus both instantaneous velocity and instantaneous speed are equal in this case. This can be understood from the following as : Consider a small displacement over a time Dt between time interval, t and $t + \Delta t$ $\therefore$ Average velocity in the interval $\Delta t = \frac{\Delta x}{\Delta t} \ldots$ (i) $\therefore$ Instantaneous velocity at instant t is, $= \underset{\Delta t \rightarrow 0}{\operatorname{Lt}} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}$Average speed $= \frac{\text{Total distance}}{\text{Total time}} = \frac{\text{Arc } PQ}{\Delta t}$ $= \underset{\Delta t \rightarrow 0}{\operatorname{Lt}} \frac{\text{Arc } PQ}{\Delta t} \ldots$(ii)where arc PQ = length of the line PQ. Now from DPQR, $PQ^{2}=PR^{2}+QR^{2}$ As $\Delta t \rightarrow 0, PQ \rightarrow QR$or $PQ \rightarrow \Delta x$From (ii), we getInstantaneous speed $= \underset{\Delta t \rightarrow 0}{\operatorname{Lt}} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}$magnitude of instantaneous velocity.