Formula: Average Velocity
$$\class{blue}{\bar v} ~=~ \frac{x_2 - x_1}{t_2 - t_1}$$
$$\class{blue}{\bar v} ~=~ \frac{x_2 - x_1}{t_2 - t_1}$$
$$x_1 ~=~ x_2 - \class{blue}{\bar v}\,(t_2 - t_1)$$
$$x_2 ~=~ x_1 + \class{blue}{\bar v}\,(t_2 - t_1)$$
$$t_1 ~=~ t_2 - \frac{x_2 - x_1}{\class{blue}{\bar v}}$$
$$t_2 ~=~ t_1 + \frac{x_2 - x_1}{\class{blue}{\bar v}}$$
Average velocity
$$ \class{blue}{\bar v} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
The average velocity of a body, e.g. an airplane or a car. It is defined as the distance traveled \(\Delta s = x_2 - x_1\) per time \(\Delta t = t_2 - t_1\):
\[ v ~=~ \frac{\Delta s}{\Delta t} \]
The sign of the average velocity determines whether the body moves to the right (positive \(v\)) or to the left (negative \(v\)).
Example: The total distance is \( \Delta s = -20 \, \text{m}\) and the time taken is \( \Delta t = 4 \text{s} \). Then the average velocity is: \[ v ~=~ \frac{-20 \, \text{m}}{4 \text{s}} ~=~ -5 \, \frac{\text m }{ \text s } \]
Since the average velocity is negative, the body moves to the left.
Start position
$$ x_1 $$ Unit $$ \mathrm{m} $$
Position of the body (on the x-axis) from which the average velocity is to be calculated.
End position
$$ x_2 $$ Unit $$ \mathrm{m} $$
Position of the body (on the x-axis) up to which the average velocity is to be calculated.
Start time
$$ t_1 $$ Unit $$ \mathrm{s} $$
The time when the body has the position \(x_1\).
End Time
$$ t_2 $$ Unit $$ \mathrm{s} $$
The time when the body has the position \(x_2\).