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# Average velocity formula

In this article learn about the average velocity formula. Now if you are interested in learning the concept of average speed and average velocity for class 11 physics and competitive exams like NEET, JEE Mains and JEE Advanced do follow the link given below.

## Average velocity definition

Average velocity is defined as the ratio of total displacement to total time. It is the average values of the velocities we know.

## Average velocity formula

Let’s talk about the average velocity formula. From the average velocity definition, we know that it is the ratio between total displacement and total time but this $v_{av}$ i.e., the average velocity formula can have different forms according to different problems. So before solving problems that ask you to find average velocity please check under which case your problem falls.

1. Case 1:-
If $X$ is the total displacement of the body and $t$ is the total time taken by the body to complete the displacement.The average velocity $V_{av}$ is given by
$$v_{av} = \frac{Total\ distance\ traveled}{total\ time\ taken} = \frac{X}{T}$$
2. Case 2:-
If we know that body has initial displacement position $x_0$ at time $t_0$ undergoes a motion and attains final displacement $x_f$ at time $t_f$ then, the average velocity is given as
$$v_{av}=\frac{x_f – x_0}{t_f – t_0}=\frac{\Delta\ x}{\Delta\ t}$$
3. Case 3:-
If we have a knowledge that $x_1, x_2, . . . . . x_n$ are the distance covered by the body for time $t_1, t_2, . . . . . t_n$. The average velocity is
$$\frac{x_1 + x_2 + . . . . . . . + x_n}{t_1 + t_2 + . …. . . + t_n}$$
4. Case 4:-
If a velocity is changing as a result of constant acceleration, the average velocity can be found by adding the initial and final velocities and dividing by 2. Here it is important to note that this formula applies only to constant acceleration cases.
Consider a body moving with uniform acceleration along a straight path. At some instant of time, initially, its velocity is $U$ m/s and at the end of t seconds let its final velocity be $V$ m/s. Hence the average velocity is given as
$$v_{av}=\frac{v+u}{2}$$
How to derive this average velocity formula
Average velocity is displacement divided by time. Let us start with the formula for displacement and divide it by t.
\begin{align} s=ut+\frac{1}{2}at^{2} \\ average \quad velocity & = \frac{ut+\frac{1}{2}at^{2}}{t} \\ & =u+\frac{1}{2}at \\ & =\frac{2u+at}{2} \\ & =\frac{u+(u+at)}{2} \end{align}
now, $v=u+at$
$$average \quad velocity = \frac{u+v}{2}$$

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