Instantaneous Velocity: Concept and Formula

Instantaneous velocity refers to the rate at which a position changes in a very short time period (almost zero). Measuring in SI units m/s. The magnitude of the instantaneous velocity is instantaneous speed. It is the same as instantaneous velocity however without any direction.

Simply put, it is the object’s velocity at that moment in time. Therefore the speed of an object or particle in motion at a particular point in time is defined as Instantaneous velocity.

If an object has uniform velocity, its standard velocity and instantaneous velocity could be the same.

It is found in the same way as average velocity however with a shorter time interval. The average velocity of a time period is the total displacement divided by the total time. The displacement also reaches zero as this time interval gets to zero. However, the limit of displacement to time is not zero and is known as instantaneous velocity.

Instantaneous Velocity: Formula

The formula is found the same way as average velocity. However, this is a very short time period. The average velocity of a time period, as we are aware, is the total displacement divided by total time. The displacement is also approaching zero when the time interval moves towards zero. However, the displacement to time ratio is not zero where the limit is concerned and this is called instantaneous velocity.

The formula for Instantaneous Velocity is equated as below:

Vi=limΔt→0  ΔxΔt=dxdt

Here, x is the function wrt time denoted by t. The Instantaneous Velocity is represented in unit of 𝑚𝑠−1. If any numerical is said to contain the function of form f(x), the determination of the instantaneous velocity can be done using the above formula.

Where,

• t is the time
• Δ𝑡 is the shorter interval.
• x is the displacement variable 
• Vi is the instantaneous velocity of the body

Instantaneous Velocity: The Concept

The rate at which a position changes in a very short time period, that is, almost zero, is referred to as instantaneous velocity. . It is measured in SI units ms-1. The instantaneous velocity’s magnitude is also called instantaneous speed. It has the same value and direction as instantaneous velocity but it doesn’t have any direction.

The velocity of an object at a given instant is called instantaneous velocity. The definition of instantaneous velocity is “The velocity at which an object is in motion at a particular point in time.”

If the object has uniform velocity, then its instantaneous velocity could be the same as its standard speed.

Instantaneous Velocity Example

How can you obtain the Instantaneous Velocity of a particle moving along a straight line for 5 seconds, with a position function x defined as 4t² + 2t + 4?

Solution to the above can be obtained as showcased below:

As mentioned above, the function x is 

x = 4t² + 2t + 4

Instantaneous Velocity can be found by using the formula below

Vi=dxdt

Replacing it with function x,

Vi=d (4t² + 2t + 4)dt

Insert the value of t as 5, we derive the instantaneous velocity

Vi=8×5+2

Vi=42𝑚𝑠−1

Therefore the instantaneous value is 42𝑚𝑠−1.

Unit of Instantaneous Velocity

The SI unit of instantaneous velocity is m/s. It is a vector quantity. It can also be determined by taking the slope of the distance-time graph or x-t graph.