# Velocity

 related topics {math, energy, light} {line, north, south}

In physics, velocity is the measurement of the rate and direction of change in position of an object. 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 meters per second (m/s or ms−1) when using the SI (metric) system.

For example, "5 meters per second" is a scalar and not a vector, whereas "5 meters per second east" is a vector. The average velocity v of an object moving through a displacement $( \Delta \mathbf{x})$ during a time interval t) is described by the formula:

The rate of change of velocity is acceleration – how an object's speed or direction changes over time, and how it is changing at a particular point in time.

## Contents

### Equation of motion

The velocity vector v of an object that has positions x(t) at time t and x(t + Δt) at time t + Δt, can be computed as the derivative of position:

Average velocity magnitude is always smaller than or equal to average speed of a given particle. Instantaneous velocity is always tangential to trajectory. Slope of tangent of position or displacement time graph is instantaneous velocity and its slope of chord is average velocity.

The equation for an object's velocity can be obtained mathematically by evaluating the integral of the equation for its acceleration beginning from some initial period time t0 to some point in time later tn.

The final velocity v of an object which starts with velocity u and then accelerates at constant acceleration a for a period of time Δt is:

The average velocity of an object undergoing constant acceleration is $\tfrac {(\mathbf{u} + \mathbf{v})}{2}$, where u is the initial velocity and v is the final velocity. To find the position, x, of such an accelerating object during a time interval, Δt, then:

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

can be used.

This can be expanded to give the position at any time t in the following way:

These basic equations for final velocity and position can be combined to form an equation that is independent of time, also known as Torricelli's equation: