# How to Find Velocity

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Velocity is the speed with a direction. It is also described as the change in position over the change in time. Velocity is the rate at which displacement changes with time. Here is how to Calculate Velocity

## How to Find the Simple Velocity

1. Write down the Velocity Formula

$\mathbf{Velocity&space;=&space;\frac{Displacement}{Time}}$ in a direction.

2. Plug the values into the formula.

Example: John walks from his home to school in 6 minutes and 40 seconds, what is his velocity?

Displacement = 200 m And Time = 6 minutes and 40 seconds = 400 s

Velocity = $\mathbf{\frac{200\&space;m}{400\&space;s}}$  North-West = 0.50 m/s North-west

## How to Find Average Velocity

1. Write the formula for Average Velocity.

$\\\mathbf{\\Average&space;Velocity&space;=&space;V_{av}&space;=&space;\frac{x_{f}-x_{i}}{t_{f}-t_{i}}&space;=&space;\frac{\bigtriangleup&space;x}{\bigtriangleup&space;t}}&space;\\&space;\\\boldsymbol{\\x_{f}&space;=&space;final\&space;position\&space;x_{i}&space;=&space;initial\&space;position}&space;\\&space;\\\mathbf{\\t_{f}&space;=&space;final\&space;time\&space;t_{i}&space;=&space;initial\&space;time}$

2. Find the distance between the start and end points.

3. Subtract the start time from the end time to find out the change in time.

4. To find out the average velocity, divide the total displacement by the total time.

Example: A car traveling due east starts at position x = 0 meters. After 8 seconds, the car is at position x = 72 meters. What was the car’s displacement?

$\\\mathbf{\\Average&space;Velocity&space;=&space;V_{av}&space;=&space;\frac{x_{f}-x_{i}}{t_{f}-t_{i}}&space;=&space;\frac{72m&space;-&space;0m}{8s&space;-&space;0s}&space;=&space;\frac{72m}{8s}&space;=&space;9&space;\frac{m}{s}\&space;East}$

## How to Find Average Velocity when Acceleration is Constant

1. Write the formula for Average Velocity if acceleration is constant.

$\\\mathbf{V_{av}&space;=&space;\frac{v_{i}+v_{f}}{2}}&space;\\&space;\\\mathbf{\\&space;v_{i}&space;=&space;initial\&space;velocity\&space;v_{f}&space;=&space;final\&space;velocity&space;}$

2. Plug the values into the formula.

For Example, A bus is traveling forward at a constant velocity of 30 m/s and then begins accelerating at a constant rate. A short time later, the velocity of the truck is 60 m/s, forward. What was the average velocity of the truck during its acceleration?

$\\\mathbf{V_{av}&space;=&space;\frac{v_{i}+v_{f}}{2}}&space;\\&space;\\\mathbf{V_{av}&space;=&space;\frac{30\&space;m/s&space;+&space;60\&space;m/s}{2}}&space;\\&space;\\\mathbf{V_{av}&space;=&space;\frac{90\&space;m/s}{2}}&space;\\&space;\\\mathbf{V_{av}&space;=&space;45\&space;m/s}$

## How to Find Velocity from Acceleration

1. Write the formula of Velocity for an accelerating object. To use this formula you will need the acceleration, and the velocity at any one point in time.

$\mathbf{V_{f}&space;=&space;V_{i}&space;+&space;at}$

2. Multiply the acceleration and change in time.

3. Add the initial Velocity and specify the direction of movement.

For Example,  A train going north at 7 m/s accelerates north at a rate of 7 m/s2. How much did the train’s velocity increase in the next 5 seconds?

Accleration a = 70 m/s2, , Change in Time t = 5 seconds
(a * t) = (7 m/s2 * 5 s) = 35 m/s increase in velocity.
Initial Velocity, $\mathbf{V_{i}}$ 7 m/s

Final Velocity,    $\\\mathbf{V_{f}&space;=&space;7&space;+&space;35\&space;m/s}&space;\\&space;\\\mathbf{V_{f}&space;=&space;42\&space;m/s}$

## How to Find Circular Velocity

The circular velocity of an object is calculated by dividing the circumference of the circular path by the time period over which the object travels.

1. Write down the formula for Circular Velocity.

2. Multiply the circular radius by 2π and divide this by the time period.

For Example, Determine the circular velocity of the earth if the distance from Sun to Earth is and the period of earth revolution is 365 days.

$\\\mathbf{\\V&space;=&space;\frac{2&space;\pi&space;r}{T}&space;=&space;\frac{(2)(3.14)(149,597,870)}{365}}&space;\\&space;\\\mathbf{\\V&space;=&space;\frac{939474623.6}{365}&space;=&space;\frac{939474623600\&space;Meters}&space;{31,536,000&space;Seconds}}&space;\\&space;\\\mathbf{\\V&space;=&space;29790.54&space;m/s}$