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When it comes to measuring motion, that is the relative passage of an object through space at a certain rate of time, several different things need to be taken into account. For example, it is not enough to know the rate of change (i.e. the speed) of the object. Scientists must also be able to assign a vector quantity; or in other words, to know the direction as well as the rate of change of that object. In the end, this is major difference between Speed and Velocity. Though both are calculated using the same units (km/h, m/s, mph, etc.), the two are different in that one is described using numerical values alone (i.e. a scalar quantity) whereas the other describes both magnitude and direction (a vector quantity).
By definition, the speed of an object is the magnitude of its velocity, or the rate of change of its position. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval. Represented mathematically, it looks like this: ν=[v]=[?] = [dr/dt]•, where speed ν is defined as the magnitude of the velocity v, that is the derivative of the position r with respect to time. The fastest possible speed at which energy or information can travel, according to special relativity, is the speed of light in vacuum (a.k.a. c = 299,792,458 meters per second, which is approximately 1079 million kilometers per hour or 671,000,000 mph).
Velocity, on the other hand, is the measurement of the rate and direction of change in the position of an object. Since it is a vector physical quantity, both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is speed, a quantity that is measured in metres per second (m/s) when using the SI (metric) system. Mathematically, this is represented as: v = Δx/Δt, where v is the average velocity of an object, (Δx) is the displacement and (Δt) is the time interval. Add to this a vector (i.e. Δx/Δt→, ←, or what have you), and you’ve got velocity!
As an example, consider the case of a bullet being fired from a gun. If we divide the overall distance it travels within a set period of time (say, one minute), than we have successfully calculated its speed. On the other hand, if we want to determine its velocity, we must consider the direction of the bullet after it’s been fired. Whereas the average speed of the object would be rendered as simple meters per second, the velocity would be meters per second east, north, or at a specific angle.
We have written many articles about speed and velocity for Universe Today. Here’s an article about formula for velocity, and here’s an article about escape velocity.
If you’d like more info on speed and velocity, check out these articles:
Speed and Velocity
Angular and Linear Velocity
We’ve also recorded an episode of Astronomy Cast about the space shuttle. Listen here, Episode 127: The US Space Shuttle.
Sources:
http://physics.info/velocity
http://en.wikipedia.org/wiki/Speed
http://en.wikipedia.org/wiki/Velocity
http://www.physicsclassroom.com/class/1dkin/u1l1d.cfm
http://www.edinformatics.com/math_science/acceleration.htm