Velocity is defined as a vector measurement of the rate and direction of motion. Put simply, velocity is the speed at which something moves in one direction. The speed of a car traveling north on a major freeway and the speed a rocket launching into space can both be measured using velocity.

As you might have guessed, the scalar (absolute value) magnitude of the velocity vector is the speed of motion. In calculus terms, velocity is the first derivative of position with respect to time. You can calculate velocity by using a simple formula that includes rate, distance, and time.

## Velocity Formula

The most common way to calculate the constant velocity of an object moving in a straight line is with this formula:

r=d/t

*r*is the rate or speed (sometimes denoted as*v*for velocity)*d*is the distance moved*t*is the time it takes to complete the movement

### Units of Velocity

The SI (international) units for velocity are m/s (meters per second), but velocity may also be expressed in any units of distance per time. Other units include miles per hour (mph), kilometers per hour (kph), and kilometers per second (km/s).

## Speed, Velocity, and Acceleration

Speed, velocity, and acceleration are all related to each other, though they represent different measurements. Be careful not to confuse these values with each other.

**Speed**, according to its technical definition, is a scalar quantity that indicates the rate of motion distance per time. Its units are length and time. Put another way, speed is a measure of distance traveled over a certain amount of time. Speed is often described simply as the distance traveled per unit of time. It is how fast an object is moving.**Velocity**is a vector quantity that indicates displacement, time, and direction. Unlike speed, velocity measures*displacement,*a vector quantity indicating the difference between an object's final and initial positions. Speed measures distance, a scalar quantity that measures the total length of an object's path.**Acceleration**is defined as a vector quantity that indicates the rate of change of velocity. It has dimensions of length and time over time. Acceleration is often referred to as "speeding up", but it really measures changes in velocity. Acceleration can be experienced every day in a vehicle. You step on the accelerator and the car speeds up, increasing its velocity.

## Why Velocity Matters

Velocity measures motion starting in one place and heading toward another place. The practical applications of velocity are endless, but one of the most common reasons to measure velocity is to determine how quickly you (or anything in motion) will arrive at a destination from a given location.

Velocity makes it possible to create timetables for travel, a common type of physics problem assigned to students. For example, if a train leaves Penn Station in New York at 2 p.m. and you know the velocity at which the train is moving north, you can predict when it will arrive at South Station in Boston.

## Sample Velocity Problem

To understand velocity, take a look at a sample problem: a physics student drops an egg off an extremely tall building. What is the egg's velocity after 2.60 seconds?

The hardest part about solving for velocity in a physics problem such as this is selecting the right equation and plugging in the right variables. In this case, two equations should be used to solve the problem: one to find the height of the building or distance the egg travels and one to find final velocity.

Start with the following equation for distance to find out how tall the building was:

d = v_{I}*t + 0.5*a*t^{2}

where *d* is distance, *v _{I}* is initial velocity,

*t*is time, and

*a*is acceleration (which represents gravity, in this case, at -9.8 m/s/s). Plug in your variables and you get:

d = (0 m/s)*(2.60 s) + 0.5*(-9.8 m/s(negative sign indicates direction downward)^{2})(2.60 s)^{2}

d = -33.1 m

Next, you can plug in this distance value to solve for velocity using the final velocity equation:

v_{f}= v_{i}+ a*t

where* v _{f} *is final velocity,

*v*is initial velocity,

_{i}*a*is acceleration, and

*t*is time. You need to solve for final velocity because the object accelerated on its way down. Since the egg was dropped and not thrown, the initial velocity was 0 (m/s).

v_{f}= 0 + (-9.8 m/s^{2})(2.60 s)

v_{f}= -25.5 m/s

So, the velocity of the egg after 2.60 seconds is -25.5 meters per second. Velocity is commonly reported as an absolute value (only positive), but remember that it's a vector quantity and has direction as well as magnitude. Usually, moving upward is indicated with a positive sign and downward with a negative, just pay attention to the object's acceleration (negative = slowing down and positive = speeding up).