metre per second

SI coherent derived unit

Name

Symbol

Derived quantity

metre per second

m s⁻¹

speed,
velocity

Definition

The metre per second, symbol m s⁻¹, is the SI coherent derived unit of speed (scalar quantity) and velocity (vector quantity).

An object with a constant speed of one metre per second moves a distance of one metre in one second.

The fixed numerical value of the speed of light in vacuum, c, is defined as 299 792 458 when expressed in the unit m s⁻¹.

$c \mspace{6mu} = 299 \mspace{4mu} 792 \mspace{4mu} 458 \mspace{6mu} \text{m} \mspace{6mu} \text{s}{^{-1}}$

Inverting this relation gives an exact expression for the metre per second in terms of the SI defining constant c :

$1 \mspace{6mu} \text{m} \mspace{6mu} \text{s}{^{-1}} \mspace{6mu} = \dfrac{c}{299 \mspace{4mu} 792 \mspace{4mu} 458}$

The effect of this definition is that one metre per second is exactly ¹⁄_{299 792 458} of the speed of light in vacuum.

Velocity

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

Velocity is a vector quantity; both magnitude and direction are needed to define it.

Speed

The speed of an object is the magnitude of its velocity. Speed is a scalar quantity.

Using SI coherent units,

$v = \dfrac{d}{t}$

where:

v is the speed in metres per second, symbol m s^-1,
d is the distance travelled in metres, symbol m,
t is the travel time in second, symbol s.

At a constant speed, an object travelling a distance of one metre in a time of one second, has a speed of 1 m s^-1.

$1 \ \text{m s}{^{-1}} = \dfrac{1 \ \text{m}}{1 \ \text{s}}$