Velocity

Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector quantity, meaning that both magnitude and direction are needed to define it (velocity vector). The scalar absolute value (magnitude) of velocity is called speed, a quantity that is measured in metres per second (m/s or m⋅s−1) in the SI (International System of Units) system. For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object is said to be undergoing an acceleration.

Definition

Average velocity

The average velocity of an object over a period of time is its change in position,

Δ

s

{\displaystyle \Delta s}

, divided by the duration of the period,

Δ

t

{\displaystyle \Delta t}

, given mathematically as

v

¯

=

Δ

s

Δ

t

.

{\displaystyle {\bar {v}}={\frac {\Delta s}{\Delta t}}.}

Instantaneous velocity

The instantaneous velocity of an object is the limit average velocity as the time interval approaches zero. At any particular time t, it can be calculated as the derivative of the position with respect to time:

v

=

lim

Δ

t

→

0

Δ

s

Δ

t

=

d

s

d

t

.

{\displaystyle {\boldsymbol {v}}=\lim _{{\Delta t}\to 0}{\frac {\Delta {\boldsymbol {s}}}{\Delta t}}={\frac {d{\boldsymbol {s}}}{dt}}.}

From this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs.