# What Is the Formula for Velocity?

By Staff WriterLast Updated Mar 30, 2020 12:42:51 AM ET Nathan E Photography/CC-BY-2.0

The basic formula for velocity is v = d / t, where v is velocity, d is displacement and t is the change in time. Velocity measures the speed an object is traveling in a given direction.

Velocity is the change in position of an object within a specific time frame. Hence, the formula for velocity can be expressed as:

Velocity = (Final position ‰ÛÒ Initial position) / Change in time

Velocity = (Xf ‰ÛÒ Xi) / t

Velocity = d / t (where d= displacement and t = change in time)

Velocity, being a vector quantity, has both magnitude and direction. Magnitude refers to size, and direction refers to the course that an item is moving along. The units that velocity is measured in are meters per second, which is commonly abbreviated as m/s.

Example:

A sailboat is in a 2,000-meter race. This boat crosses the starting line when it has already achieved full speed. It reaches the finish line in exactly three minutes and 20 seconds (200 seconds). To determine the velocity of the sailboat, follow the equation below.

Solution:

Velocity = (Final position ‰ÛÒ initial position) / Change in time

Velocity = (2000m ‰ÛÒ 0m) / 200 sec

Velocity = 10m/s in the direction of the finish line.

Average Speed Vs. Average Velocity

Average speed is an object's net change in distance per unit of time. Speed describes how fast an object is moving in a given direction. Average velocity is the net change in displacement per unit of time. Velocity refers to the rate that an object is changing positions. Speed is generally measured while an object is traveling in one direction, whereas velocity can be measured by how far an item travels from its starting position. The equations below illustrate how to find the averages of these numbers.

Average speed = Total distance traveled / total time taken

Average velocity= Total object displacement / total time taken

The example below illustrates the equations for finding these values.

A car is traveling north at a speed of 30 miles per hour for two hours. Then, it travels at the same speed (30 miles per hour) for one hour, but it is traveling south instead of north. Determine the average speed and velocity using the equation below.

Solution:

The total distance traveled is (30 miles/hour x 2 hours) + (30 miles/hour x 1 hour) = 90 miles

The total time taken is 3 hours.

Average Speed = Total distance/ total time

Average Speed = T90miles / 3 hours

Average Speed = T30miles per hour

Or, consider it this way:

Average velocity = Total displacement / total time

Displacement to the north = (30 miles/hour x 2 hours) - (30 miles/hour x 1 hour)

Displacement to the north = 30 miles

Average Velocity = 30 miles / 3 hours

Average Velocity = 10 miles per hour

Angular Velocity

Angular velocity is the measurement of angular displacement of an object in a circular path per unit time. The direction of angular velocity is limited to clockwise and counterclockwise directions.

Angular velocity = Angle of rotation (theta) / time

The basic unit for angular velocity is radians per second. However, in practice, most people prefer the use of revolutions per min (RPM). In this case, one revolution covers a distance of 2pi radians. For a complete revolution, angular velocity = 2pi radians / time in seconds.

Example:

An object moving in a circular path completes one revolution in 4 seconds. Calculate its angular velocity.

Solution:

Angular velocity = Angle of rotation / time

Angular velocity = 2pi radians / time

Angular velocity = 2x3.14 / 4

Angular velocity = 1.57 radians per second (rad/s)