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+Δt
∴ Average velocity in the interval Δt=

Δx

Δt

... (i)
∴ Instantaneous velocity at instant t is,
=

Lt

Δt→0

Δx

Δt

=

dx

dt

Average speed =

Total‌distance

‌Total‌time

=

‌Arc‌P‌Q

Δt

=

Lt

Δt→0

‌Arc‌P‌Q

Δt

...(ii)
where arc PQ = length of the line PQ.
Now from DPQR,
PQ2=PR2+QR2
As Δt→0,PQ→QR
or PQ→Δx
From (ii), we get
Instantaneous speed =

Lt

Δt→0

Δx

Δt

=

dx

dt

magnitude of instantaneous velocity.