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What is Displacement Help

By — McGraw-Hill Professional
Updated on Oct 25, 2011

Displacement

Displacement is almost the same thing as distance, but not quite. Displacement is defined along a straight line in a certain direction. But distance can be measured any which way. We might say that Minneapolis, Minnesota is displaced 100 km from Rochester, Minnesota “as the crow flies,” or along a straight line. If you were to drive along US Route 52, however, the distance is closer to 120 km, because that highway does not follow a straight path from Rochester to Minneapolis.

Displacement as a Vector

Displacement is a vector quantity because it has magnitude and direction. A displacement vector is denoted by a lowercase boldface letter such as d. Displacement magnitude (distance) is denoted by a lowercase italic letter such as d .

The displacement vector d of Minneapolis, expressed with respect to Rochester, is about 100 km in a northwesterly direction “as the crow flies.” Expressed as a compass bearing, the direction of d is around 320°, measured clockwise from north. But if we speak about driving along Route 52, we can only talk about distance, because the road is not straight or level all the way. The distance of Minneapolis from Rochester, measured along Route 52, is a scalar, and is equal to roughly d = 120 km.

How Displacement is Determined

Distance can be determined by mechanical measurement, or by inferring it with observations and calculations. In the case of a car or truck driving along Route 52, distance is measured with an odometer that counts the number of wheel rotations, and multiplies this by the circumference of the wheel. In other real-world scenarios, distance can be measured with a meter stick , by triangulation, or by more sophisticated means such as the use of the Global Positioning System (GPS).

The direction component of a displacement vector is determined by measuring one or more angles or coordinates relative to a reference axis. In the case of a local region on the earth’s surface, direction can be found by specifying the azimuth, which is the compass bearing (the angle around the horizon clockwise relative to true north). That is the scheme used by hikers and back-packers. In three-dimensional space, direction angles are used. There are various ways in which these can be defined, but we don’t need to get into that here.

Find practice problems and solutions for these concepts at the Movement Practice Test.

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