Problems on Instantaneous Velocity

A speedometer shows different Speeds at different instants

This is because vehicles don't travel with constant Speed at all times

At any given instance what we read from the speedometer of the vehicle is instantaneous speed

Instantaneous speed can be defined as the speed of an object at a particular time or instant

And if we include the direction with the instantaneous Speed, we get the Instantaneous Velocity of the object

As per definition, Instantaneous Velocity is the rate of change of Displacement per unit Time

We can express it mathematically as,


To understand the concept better, let us solve a problem using this equation

Problem An object moving with a Velocity . Calculate the Displacement of the object between and

Solution As per definition, we know that Velocity is the rate of change of position of an object in unit Time

Therefore we can say,

Velocity We can also say that,

Integrating L.H.S with limits to and integrating R.H.S with limits Time to ,

Change in displacement

Therefore, the Displacement made by the object in time to is


Instantaneous Velocity is the Velocity of an object in Motion at a specific point in Time

Instantaneous velocity can be mathematically expressed as, Where,

The End