# Average Velocity calculator

Note
• Enter the values of the two known variables in the text boxes
• Leave the text box empty for the variable you want to solve for
• Click on the calculate button.
The Average velocity formula used for solving the question is
$\bar{v}=\frac {v_f + v_i}{2}$
$v_f= 2 \bar{v} - v_i$
$v_i= 2 \bar{v} - v_f$

## What is average velocity

Average velocity is defined as the ratio of change in displacement $\Delta x$ of the object and time interval $\Delta t= t_2 -t_1$.
$\bar{v} = \frac {\Delta x}{\Delta t}$
If the body is moving in straight line with constant acceleration, Average velocity over a time interval is also defined as the average of the velocity of the starting point and ending point. So if $v_i$ be the initial velocity and $v_f$ be the final velocity for the particle moving in straight with constant acceleration, then average velocity is given
$\bar{v}=\frac {v_f + v_i}{2}$
where
$\bar{v}$ -> Average velocity
$v_i$ -> initial velocity
$v_f$ -> final velocity
Average velocity is a vector quantity and SI unit is meter/sec

Example of Few questions where you can use this formula
Question 1
A object start with velocity 2 m/s and attained a velocity 10 m/s in 4 sec.Find the average velocity
Solution
Given $v_i=2 \ m/s$, $v_f=10 \ m/s$, $\bar{v}$=?
Now average velocity is given
$\bar{v}=\frac {v_f + v_i}{2}= \frac { 2 + 10}{2} = 6 \ m/s$

Question 2
A object start with velocity 1 m/s and average velocity for the period of time is 5 m/s. Find the final velocity.
Solution
Given $v_i=2 \ m/s$, $v_f$=?, $\bar{v}= 5 \ m/s$
Now average velocity is given
$\bar{v}=\frac {v_f + v_i}{2}$
Rearranging for Final velocity
$v_f = 2 \bar{v} - v_i = 2 \times 5 -1 = 9 \ m/s$

## How the Average Velocity Calculator works

1. If $v_i$ and $v_f$ are given
$\bar{v}=\frac {v_f + v_i}{2}$
2. If $v_i$ and $\bar{v}$ are given
$v_f= 2\bar{v} - v_i$
2. If $v_f$ and $\bar{v}$ are given
$v_i= 2\bar{v} - v_f$

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