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Velocity Help

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By McGraw-Hill Professional
Updated on Sep 4, 2011

Introduction to Velocity

Velocity consists of two independent components: speed and direction . The direction can be defined in one dimension (either way along a straight line), in two dimensions (within a plane), or in three dimensions (in space). Some physicists get involved with expressions of velocity in more than three spatial dimensions.

Velocity Is A Vector

Because velocity has both magnitude and direction components, it is a vector quantity. You can’t express velocity without defining both these components. In the earlier example of a car driving along a highway from one town to another, its speed might be constant, but the velocity changes nevertheless. If you’re moving along at 25 m/s and then you come to a bend in the road, your velocity changes because your direction changes.

Vectors can be illustrated graphically as line segments with arrowheads. The speed component of a velocity vector is denoted by the length of the line segment, and the direction is denoted by the orientation of the arrow.

Fig. 7.6 . Velocity vectors a, b , and c for a car at three points ( A , B , and C ) along a road.

In Fig. 7-6, three velocity vectors are shown for a car traveling along a curving road. Three points are shown, called A , B , and C . The corresponding vectors are a, b , and c . Both the speed and the direction of the car change with time.

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. 7-6, 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.

Practice problems of these concepts can be found at: Mass, Force, And Motion Practice Problems

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