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Velocity

The velocity of an object is its total speed in a particular direction. Since velocity is defined as a vector, both speed and direction are required to define it. more...

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Definition of Velocity

Velocity is a non physical quantity of an object's motion. Velocity is speed that has a clearly stated direction. For example, "5 metres per second" is not a vector, where as "5 meters per second east" is a vector. If the motion is in a straight line in only one direction, it is the same as speed. The average velocity (v) of an object moving a displacement (s) in a straight line during a time interval (t) is described by the formula:

$\text{[math]}$

Formal description

Velocity (symbol: v) is a vector measurement of the rate of change of displacement from a fixed point. The scalar absolute value (magnitude) of velocity is speed. Velocity can also be defined as rate of change of displacement or just as the rate of displacement. It is a vector quantity with dimension LT^(-1). In the SI (metric) system, it is measured in meters per second.

The instantaneous velocity vector (v) of an object that has position at time (t) is given by x(t) can be computed as the derivative:

$\text{[math]}$ The equation for an object's velocity can be obtained mathematically by taking the integral of the equation for its acceleration beginning from some initial period time $t 0$ to some point in time later $t n$ .

The final velocity v₂ of an object which starts with velocity v₁ and then accelerates at constant acceleration a for a period of time t is:

$\text{[math]}$ The average velocity of an object undergoing constant acceleration is $\text{[math]}$

When only the object's initial velocity is known, the expression,

$\text{[math]}$ can be used. These basic equations for final velocity and displacement can be combined to form an equation that is independent of time, also known as Torricelli's equation:

$\text{[math]}$ The above equations are valid for both classical mechanics and special relativity. Where classical mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in classical mechanics, all observers agree on the value of t and the transformation rules for position create a situation in which all non-accelerating observers would describe the acceleration of an object with the same values. Neither is true for special relativity. In other words only relative velocity can be calculated.