Velocity and Average Velocity

It is common to start running towards the bus-stop instead of walking when we get late.

As we approach the bus-stop our pace of Running slows down

We can say that our pace of motion changed drastically between the initial and final points.

Displacement is defined as the shortest distance between the initial and final points.

How fast or slow an object moves in a particular direction is given by its Velocity

Velocity can be defined as the change in Displacement of an object in unit Time

This can be mathematically expressed as, $\text{Velocity}=\frac{\text{Displacement}}{\text{Time}}$

But the Velocity of an object in Motion is not constant throughout the journey

For example, if the Velocity of an object is said to be $20m/s$

It is not mandatory that the Velocity of the object was $20m/s$ all throughout the journey

It could have covered 90m in 5s, and the next 110m in 5s

The ratio of the Total Displacement and the Total Time will give the Average Velocity of the object

It is a vector quantity and has units of m/s

Let us see how the Average Velocity of an object can be expressed mathematically

Suppose an object is at position $x_1$ at Time $t_1$

The object moves to point $x_2$ at Time $t_2$

The change in the position is given by, $△x=x_2-x_1$

The time taken to cover the distance is given by, $△t=t_2-t_1$

Therefore, as per definition, Average Velocity is Total Displacement by Total Time or, $\text{Average Velocity}=\frac{\text{Total Displacement }}{\text{Total Time}}$

Expressing Average Velocity $v_{average}$ mathematically, ${v}_{average}=\frac{x_2-x_1}{t_2-t_1}$

It can also be written as, ${v}_{\text{average}}=\frac{△x}{△t}$

The Average Velocity tells us how fast an object has been moving over a given Time interval

But does not tell us how fast it moves at different instants of time during that interval

Revision

Velocity can be defined as the rate of change of Displacement of an object in unit Time. The unit of Velocity is given in m/s

$v=\frac{x}{t}$ Where, $$\begin{gathered} v=\text{Velocity} \\ x=\text{Displacement} \\ t=\text{Time} \end{gathered}$$

Average Velocity is defined as the ratio of Total Displacement made by the object in Total Time. It is a vector quantity and has units of m/s

${v}_{average}=\frac{△x}{△t}$ Where, ${v}_{average}=\text{Average Velocity}$

The End