Most people take velocity and speed to be the same thing. While it might be true in certain, ideal circumstances, as a physicist and mathematician, it’s not entirely the same thing.

## What is Velocity?

In the simplest terms, Velocity is object’s speed in a particular direction. In Mathematics, we describe velocity as the rate of change in displacement.

Velocity is direction sensitive. Unlike speed which only considers distance covered in a certain amount of time. Therefore, the only time that speed is the same as velocity is when the object travels in a straight line.

To calculate velocity, we calculate the displacement from the starting point to the finish point and divide that by the time covered. **Displacement** is the distance in a straight line or the change in position.

## Velocity Formula

## Examples:

For this particular tutorial, I’ll give 2 examples to make sure you understand the relationship between speed and velocity and why the two are often confused to be the same thing.

#### Example 1

An object moves in a straight line from position A to position B, a distance of 300 meters in 20 seconds.

a) What is the speed of that object? b) What is the velocity of that object?

In this case, since the object traveled in a straight line, the the total distance covered is equal to the displacement of the object between the starting point and the finish point.

Therefore,

In Example 1, the velocity and speed is the same, but the velocity has direction in it. The next example will change everything.

#### Example 2:

The road from home to school is a winding road that totals to a distance of 46km. If it took takes me 3 hours to walk to school along the road. @)At what speed did I walk to school? b)What was my velocity from home to school?

In this case, since there’s a directional issue, the displacement and the distance will not be the same. This is where the difference between speed and velocity is clearly seen.

There are instances where velocity can be zero whereas speed is 30km/h. If you run around a race track and finish at the same exact point you started, your displacement would be zero and hence your velocity would be zero too!