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 a particular direction, such as the speed of a car traveling north on a major freeway, or the speed a rocket travels as it launches into space. The scalar (absolute value) magnitude of the velocity vector is the speed of the 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 uses 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 the formula:

r=d/t

where

*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 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 vs. Velocity and Acceleration

Speed, velocity, and acceleration are all related to each other. Remember:

**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**, by definition, is a vector quantity that indicates distance per time and direction. Like speed, its units are length and time, but direction is also involved in the equation. Velocity measures displacement over time, as opposed to distance.

**Acceleration **is defined in technical terms as a vector quantity that indicates the rate of change of velocity. It has dimensions of length and time. Study.com puts it in simpler terms: "Acceleration is often called 'speeding up,' though it would more accurately be referred to as 'velocitying up.'" The everyday experience of acceleration is in a vehicle. You step on the accelerator and the car speeds up as increasing force is applied to the drive train by the engine.

## Why Velocity Matters

Velocity measures motion starting in one place and heading toward another place. In other words, you use measures of velocity to determine how quickly you (or anything in motion) will arrive at a destination from a given location.

Measures of velocity allow you to (among other things) create timetables for travel. 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, it can be helpful to peruse a sample problem. For example, 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 is selecting the right equation. In this case, two equations may be used to solve the problem.

Use the equation:

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 (due to gravity, in this case). So, you would have:

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 equation:

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

where v_{f} is final velocity, v_{i} is initial velocity, a is acceleration, and t is time. Since the egg was dropped and not thrown, the initial velocity is 0.

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. Although it's common to report velocity as a simple value, remember it's a vector and has direction as well as magnitude. Usually, moving upward is indicated with a positive sign, and down carries a negative sign.