Rectilinear Motion - Instantaneous Velocity

Instantaneous velocity is a core concept in the study of motion. It tells us how fast and in what direction an object is moving at a specific moment. This measurement is crucial because a moving object's speed often changes. It is mathematically defined using a limit of the average velocity over a very short time

Instantaneous velocity of an object is its velocity at a given instant of time. It is defined as the limiting value of the average velocity of the object over a small time interval (Δt) around t when the value of the time interval (Δt) goes to zero.

\[\vec{\mathrm{v}}=\lim_{\Delta t\to0}\left(\frac{\Delta\vec{x}}{\Delta t}\right)=\frac{d\vec{x}}{dt}\]

Car Speedometer: The reading on a car's speedometer (which indicates speed, the magnitude of velocity) at any moment is the instantaneous speed. If you glance down and it says 60 km/h, that is the instantaneous speed at that instant.