# Instantaneous Velocity Formula

Instantaneous velocity, as the name suggests, refers to the velocity at a particular instance. This write-up highlights the definition of instantaneous velocity, equation, and a problem along with its solution.

Omkar Phatak

Last Updated: Sep 21, 2018

What is Instantaneous Velocity?

One of the attributes of velocity is that it is a vector quantity. As we all know, a vector is any physical quantity whose description is incomplete without a specification of direction associated with it.

Average Velocity (V) =

**Displacement ÷ Time = ΔS ÷ ΔT**

where,

**ΔS is the total displacement**

ΔT is the period for which displacement occurs

ΔT is the period for which displacement occurs

Formula for Instantaneous Velocity

The concept of an instance is best understood mathematically in terms of a limit. Here is the formula in terms of a limit:

Instantaneous Velocity =

The value at any particular moment of motion can be calculated by taking the derivative of equation of motion for displacement, and substituting the value of time in the result.

Instantaneous Velocity =

**Lim**

_{ΔT → 0}ΔS / ΔT = dS / dTThe value at any particular moment of motion can be calculated by taking the derivative of equation of motion for displacement, and substituting the value of time in the result.

Calculating Instantaneous Velocity

In order to calculate the instantaneous velocity of an object, we need to know its displacement and the time required.

Problem

The equation of motion for a particle (in motion) is

**6t**. Find the instantaneous velocity of the particle at^{2}+ 2t + 1**t = 5s**.Solution

Instantaneous Velocity (at t = 5) = [dS ÷ dt]

_{t = 5}= [12t + 2]_{t = 5}= 62 m/s