Physlib.Units.WithDim.Speed

The type `DimSpeed` represents the set of speeds as dimensionful quantities. It is defined as the type of functions that assign a non-negative real number $\mathbb{R}_{\ge 0}$ to each system of units, consistent with the physical dimension of speed $L \cdot T^{-1}$, where $L$ and $T$ denote the dimensions of length and time respectively. Specifically, an element of `DimSpeed` satisfies the scaling relation across different unit choices according to the dimension $L \cdot T^{-1}$.

The constant `DimSpeed.oneMeterPerSecond` represents the dimensionful quantity corresponding to a speed of $1 \text{ m/s}$. It is an element of the type $\text{DimSpeed}$, which consists of functions mapping unit choices to values consistent with the physical dimension $L \cdot T^{-1}$. Specifically, it is defined as the unique dimensionful quantity that evaluates to $1$ when the system of units is the International System of Units (SI).

The constant `DimSpeed.oneMilePerHour` represents the dimensionful quantity corresponding to a speed of $1 \text{ mph}$ (miles per hour). It is an element of `DimSpeed`, the type of quantities with physical dimension $L \cdot T^{-1}$. Mathematically, it is defined as the dimensionful quantity (a function mapping unit choices to values) that evaluates to $1$ in a system of units where the unit of length is miles and the unit of time is hours.

The constant `DimSpeed.oneKilometerPerHour` represents the dimensionful quantity corresponding to a speed of $1 \text{ km/h}$. It is an element of `DimSpeed`, the type of quantities with physical dimension $L \cdot T^{-1}$. Mathematically, it is defined as the dimensionful quantity (a function mapping unit choices to values) that evaluates to $1$ in a unit system where the unit of length is kilometers and the unit of time is hours.

The constant `DimSpeed.oneKnot` represents the dimensionful physical quantity corresponding to a speed of $1$ knot. It is an element of the type `DimSpeed`, which encompasses quantities with the physical dimension $L \cdot T^{-1}$. Mathematically, it is defined as the dimensionful quantity (a function mapping unit choices to values) that evaluates to $1$ in a system of units where the unit of length is nautical miles and the unit of time is hours.

The constant `DimSpeed.speedOfLight` represents the dimensionful quantity corresponding to the speed of light, $c$. It is an element of the type of quantities with physical dimension $L \cdot T^{-1}$. Specifically, it is defined as the dimensionful quantity that, when evaluated in the International System of Units (SI), equals $299,792,458$, representing $299,792,458 \text{ m/s}$.

The dimensionful speed quantity $1 \text{ m/s}$ evaluates to $1$ when the system of units used is the International System of Units (SI).

The numerical value of the dimensionful quantity representing 1 mile per hour, when evaluated in the International System of Units (SI), is $0.44704$. In the SI system, where the unit of speed is meters per second, this represents the conversion $1 \text{ mph} = 0.44704 \text{ m/s}$.

The value of the dimensionful speed $1 \text{ km/h}$ when evaluated in the International System of Units (SI) is equal to $5/18$.

The value of the dimensionful quantity representing a speed of one knot, when evaluated in the International System of Units (SI), is equal to $463/900$. Given that the SI unit for speed is meters per second, this means $1 \text{ knot} = \frac{463}{900} \text{ m/s}$.

In the International System of Units (SI), the numerical value of the dimensionful speed of light $c$ is equal to $299,792,458$.

The dimensionful speed of one knot is equal to the product of the scalar $1.852 \in \mathbb{R}_{\ge 0}$ and the dimensionful speed of one kilometer per hour. Mathematically, this is expressed as $1 \text{ knot} = 1.852 \cdot (1 \text{ km/h})$, where the multiplication represents the scalar action of non-negative reals on the type of dimensionful speeds.

The dimensionful quantity representing a speed of $1 \text{ km/h}$ is equal to the product of the scalar $\frac{250}{463} \in \mathbb{R}_{\ge 0}$ and the dimensionful quantity representing a speed of $1 \text{ knot}$: $$1 \text{ km/h} = \frac{250}{463} \cdot (1 \text{ knot})$$

The dimensionful speed of one meter per second, denoted as $1 \text{ m/s}$, is equal to the scalar multiplication of the constant $\frac{3125}{1397}$ and the dimensionful speed of one mile per hour, denoted as $1 \text{ mph}$: $$1 \text{ m/s} = \frac{3125}{1397} \cdot 1 \text{ mph}$$ Here, $1 \text{ m/s}$ and $1 \text{ mph}$ are elements of the type `DimSpeed` representing quantities with physical dimension $L \cdot T^{-1}$.