HOW VELOCITY IS DETERMINED
 

Velocity can be measured by using a speedometer in combination with some sort of device that indicates the instantaneous direction of travel. In a car, this might be a magnetic compass. In a strict sense, however, even a speedometer and a compass don’t tell the whole story unless you’re driving on a flat plain or prairie. In midstate South Dakota, a speedometer and compass can define the instantaneous velocity of your car, but when you get into the Black Hills, you’ll have to include a clinometer (a device for measuring the steepness of the grade you’re ascending or descending).

Two-dimensional direction components can be denoted either as compass (azimuth) bearings or as angles measured counterclockwise with respect to the axis pointing “east.” The former system is preferred by hikers and navigators, whereas the latter scheme is preferred by theoretical physicists and mathematicians. In Fig. 1, the azimuth bearings of vectors a, b, and c are approximately 90, 120, and 45 degrees, respectively. In the mathematical model, they are about 0, -30 (or 330), and 45 degrees, respectively.
A three-dimensional velocity vector consists of a magnitude component and two direction angles. Celestial latitude and longitude or right ascension and declination are used commonly to denote the directions of velocity vectors.

Fig. 1. Velocity vectors a, b, and c for a car at three points (A, B, and C) along a road.