Velocity is defined as a vector measurement of the rate and direction of motion or, in simpler terms, the rate and direction of the change in the position of an object. 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.

### How Is Velocity Calculated?

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

r=d/twhere

ris the rate, or speed (sometimes denoted asv, for velocity)dis the distance movedtis 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).

### Relating Velocity, Speed, and Acceleration

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

- Speed is a scalar quantity that indicates the rate of motion distance per time. Its units are length/time.
- Velocity is a vector quantity that indicates distance per time and direction. Like speed, its units are length/time, but direction is also cited.
- Acceleration is a vector quantity that indicates the rate of change of velocity. It has dimensions of length/time.

### Why Does Velocity Matter?

Velocity measures motion starting in one place and heading toward another place.

In other words, we use measures of velocity to determine how quickly we (or anything in motion) will arrive at a destination from a given location. Measures of velocity allow us to (among other things) create timetables for travel. For example, if a train leaves Penn Station in New York at 2:00 and we know the velocity at which the train is moving north, we can predict when it will arrive at South Station in Boston.

### Sample Velocity 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 is selecting the right equation. In this case, two equations may be used to solve the problem.

Using the equation:

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

where d is distance, v_{I} is initial velocity, t is time, a is acceleration (due to gravity, in this case)

d = (0 m/s)*(2.60 s) + 0.5*(-9.8 m/s^{2})(2.60 s)^{2}

d = -33.1 m (negative sign indicates direction downward)

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

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.