Mean speed and pace

Speed of a motion is the time rate of length change, that is, the length interval with respect to a timeline interval without regard to direction. Pace of a motion is the space rate of time change, that is, the time interval with respect to a baseline interval without regard to direction.

The symbol for speed is v = Δst and for pace is u = Δts. Instantaneous speed is ds/dt. Placepoint pace is dt/ds.

There are two kinds of mean speed or pace: the time mean and the space mean. The time mean is the arithmetic mean if the denominators are a common time interval. The space mean is the arithmetic mean if the denominators are a common space interval. The time mean is the harmonic mean if the denominators are a common space interval. If the denominators are a common time interval, the space mean is the harmonic mean.

The time mean speed (TMS) is the arithmetic mean of speeds with a common time interval. The space mean pace (TMP) is the harmonic mean of paces with a common time interval. For example, the travel distance for vehicles on a highway during a time period is measured. The time mean speed or pace may then be calculated.

The space mean pace (SMP) is the arithmetic mean of paces with a common space interval. The space mean speed (SMS) is the harmonic mean of speeds with a common space interval. For example, the travel time for vehicles over a given length of highway is measured. The space mean speed or pace may then be calculated.

If the speed of light is measured by reflection between two points, the result is a space mean speed of the transmission and reflection speeds. There may be speed from many reflections. The second postulate of relativity says that all of these speeds should be equal.

The travel distance for vehicles over a time interval may be measured by probe vehicles that record odometer readings for two points in time. The travel time for vehicles over a length of highway may be measured by a time stamp for each vehicle at two points on the highway. This may be done with sensors placed a short distance apart so the consecutive time stamps are for the same vehicle.

Spot speeds are time speeds of vehicles at a point on the roadway. They may be measured by a radar device on the roadside. The mean speed for spot speeds is a time mean speed.

In symbols:

If a beam of light is reflected back from a known distance, the two-way space mean speed of light may be calculated. From measurements such as this the one-way speed of light in a vacuum has been postulated to be a constant equal to 299,792,458 m/s.