Velocity is generally defined as the rate of change of position of an object with respect to time, including direction, so it is a vector quantity. Instantaneous velocity specifically refers to the velocity of an object at a particular instant in time. It is the rate at which the position of the object changes at that very moment, mathematically expressed as the derivative of position with respect to time:
Instantaneous velocity=limΔt→0ΔxΔt=dxdt\text{Instantaneous velocity}=\lim_{\Delta t\to 0}\frac{\Delta x}{\Delta t}=\frac{dx}{dt}Instantaneous velocity=Δt→0limΔtΔx=dtdx
This means instantaneous velocity shows how fast and in what direction an object is moving exactly at a given point in time, as opposed to average velocity, which is calculated over a finite time interval. Instantaneous velocity can be visualized as the slope of the tangent to the position-time graph at a specific time. In summary:
- Velocity is the general concept of the rate of change of position.
- Instantaneous velocity is the velocity at a specific instant, found by taking the limit of the average velocity as the time interval approaches zero.
Both are vector quantities and include direction as well as magnitude.
