In one way or the other humans move from one place to the other, this form of movement is also applicable to any sort of object. Today we will be discussing the definition, formula, differences, and examples of distance and displacement. Show
What is a distance?A distance can be defined as the total movement of an object with no regard to direction. We can also say distance is the amount of ground an object has covered from its starting point to its final destination. A distance can also be seen as a scalar quantity, that is, the distance of an object does not depend on the direction of its motion. It is the complete path traveled by an object. We can use the below formula to calculate distance: Distance[d] = Speed[s] x Time[t]Read more: The Three Newton’s laws of motion What is displacement?Displacement simply refers to the change in position of a particular object. For instance, an object moves from point A to point B, through that process displacement has occurred. Displacement represents a vector quantity and it has both magnitude and direction. The below formula can be used to calculate displacement Displacement[s] = velocity[v] x Time[t]Differences Between Distance and DisplacementThe table below will show us the differences between distance and displacement:
Read more: Relationship between Force and Motion To know the difference between distance and displacement, you should understand the definition which has been stated above. Also, you should understand that a vector quantity such as displacement is direction-aware and scalar quantity such as distance is ignorant of direction. That is if an object changes its direction of motion, displacement record the change; moving to the opposite direction effectively begins to cancel the displacement that was once recorded. Watch the video below to learn more on distance and displacement:Read more: How Force changes the State of Motion Examples and calculationsA good example of distance and displacement, since displacement is a vector quantity, which is the object’s overall change in position. Let say an object moves from 4meter east, 2meter south, 4meter west, and 2meter north. The total distance in which the object moved is 12meters, [distance=12] the displacement in the motion of the object. So, [displacement=0], this is because displacement must give attention to direction. it is a vector quantity, so, the 4meter east eliminates the 4meter west and the 2meter south Cancel the 2meter north. Another good example of distance and displacement can be seen in the position of a person that moves from point A to B to C to D. to determine the displacement and the distance traveled by the person In three minutes. The person covers a distance of; Distance from A – B = 180m B – C = 140m C – D = 100M So, the distance the person covered is [180140100] = 420m The displacement will be 140m. Read more: Understanding buoyancy Mr. John travels 290 miles north then back-tracks to the south for 105 miles to pick yogurt in the grocery store. What is Mr. John’s total displacement? SolutionMr. John starting point Xi = 0 His final position XF is the distance travelled N minus the distance south Calculating displacement, i.e., ‘’d’’ D =X = [XF Xi] D = [290 mi N 105 mi N]0 D = 185 min. Read more: Forms of energy: kinetic and potential energy That is all for this article, where the definition, formula, differences, and examples of distance and displacement are being discussed. I hope you got a lot from the reading, if so, kindly share with other students. Thanks for reading, see you around.
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). Since spatial cognition is a rich source of conceptual metaphors in human thought,[1] the term is also frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation (as exemplified by distance between people in a social network). Most such notions of distance, both physical and metaphorical, are formalized in mathematics using the notion of a metric space. In the social sciences, distance can refer to a qualitative measurement of separation, such as social distance or psychological distance. Distances in physics and geometryThe distance between physical locations can be defined in different ways in different contexts. Straight-line or Euclidean distanceThe distance between two points in physical space is the length of a straight line between them, which is the shortest possible path. This is the usual meaning of distance in classical physics, including Newtonian mechanics. Straight-line distance is formalized mathematically as the Euclidean distance in two- and three-dimensional space. In Euclidean geometry, the distance between two points A and B is often denoted | A B | {\displaystyle |AB|} . In coordinate geometry, Euclidean distance is computed using the Pythagorean theorem. The distance between points (x1, y1) and (x2, y2) in the plane is given by:[2][3] d = ( Δ x ) 2 + ( Δ y ) 2 = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 . {\displaystyle d={\sqrt {(\Delta x)^{2}+(\Delta y)^{2}}}={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}.} Similarly, given points (x1, y1, z1) and (x2, y2, z2) in three-dimensional space, the distance between them is:[2]d = ( Δ x ) 2 + ( Δ y ) 2 + ( Δ z ) 2 = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 + ( z 2 − z 1 ) 2 . {\displaystyle d={\sqrt {(\Delta x)^{2}+(\Delta y)^{2}+(\Delta z)^{2}}}={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}}.} This idea generalizes to higher-dimensional Euclidean spaces.MeasurementThere are many ways of measuring straight-line distances. For example, it can be done directly using a ruler, or indirectly with a radar (for long distances) or interferometry (for very short distances). The cosmic distance ladder is a set of ways of measuring extremely long distances. Shortest-path distance on a curved surfaceAirline routes between Los Angeles and Tokyo approximately follow a direct great circle route (top), but use the jet stream (bottom) when heading eastwards. The shortest route appears as a curve rather than a straight line because the map projection does not scale all distances equally compared to the real spherical surface of the Earth.The straight-line distance between two points on the surface of the Earth is not very useful for most purposes, since we cannot tunnel straight through the Earth's mantle. Instead, one typically measures the shortest path along the surface of the Earth, as the crow flies. This is approximated mathematically by the great-circle distance on a sphere. More generally, the shortest path between two points along a curved surface is known as a geodesic. The arc length of geodesics gives a way of measuring distance from the perspective of an ant or other flightless creature living on that surface. Effects of relativityIn the theory of relativity, because of phenomena such as length contraction and the relativity of simultaneity, distances between objects depend on a choice of inertial frame of reference. On galactic and larger scales, the measurement of distance is also affected by the expansion of the universe. In practice, a number of distance measures are used in cosmology to quantify such distances. Other spatial distancesManhattan distance on a gridUnusual definitions of distance can be helpful to model certain physical situations, but are also used in theoretical mathematics:
Metaphorical distancesMany abstract notions of distance used in mathematics, science and engineering represent a degree of difference or separation between similar objects. This page gives a few examples. Statistical distancesIn statistics and information geometry, statistical distances measure the degree of difference between two probability distributions. There are many kinds of statistical distances, typically formalized as divergences; these allow a set of probability distributions to be understood as a geometrical object called a statistical manifold. The most elementary is the squared Euclidean distance, which is minimized by the least squares method; this is the most basic Bregman divergence. The most important in information theory is the relative entropy (Kullback–Leibler divergence), which allows one to analogously study maximum likelihood estimation geometrically; this is an example of both an f-divergence and a Bregman divergence (and in fact the only example which is both). Statistical manifolds corresponding to Bregman divergences are flat manifolds in the corresponding geometry, allowing an analog of the Pythagorean theorem (which holds for squared Euclidean distance) to be used for linear inverse problems in inference by optimization theory. Other important statistical distances include the Mahalanobis distance and the energy distance. Edit distancesIn computer science, an edit distance or string metric between two strings measures how different they are. For example, the words "dog" and "dot", which differ by just one letter, are closer than "dog" and "cat", which have no letters in common. This idea is used in spell checkers and in coding theory, and is mathematically formalized in a number of different ways, including Levenshtein distance, Hamming distance, Lee distance, and Jaro–Winkler distance. Distance in graph theoryIn a graph, the distance between two vertices is measured by the length of the shortest edge path between them. For example, if the graph represents a social network, then the idea of six degrees of separation can be interpreted mathematically as saying that the distance between any two vertices is at most six. Similarly, the Erdős number and the Bacon number—the number of collaborative relationships away a person is from prolific mathematician Paul Erdős and actor Kevin Bacon, respectively—are distances in the graphs whose edges represent mathematical or artistic collaborations. In the social sciencesIn psychology, human geography, and the social sciences, distance is often theorized not as an objective numerical measurement, but as a qualitative description of a subjective experience.[4] For example, psychological distance is "the different ways in which an object might be removed from" the self along dimensions such as "time, space, social distance, and hypotheticality".[5] In sociology, social distance describes the separation between individuals or social groups in society along dimensions such as social class, race/ethnicity, gender or sexuality. Mathematical formalizationMost of the notions of distance between two points or objects described above are examples of the mathematical idea of a metric. A metric or distance function is a function d which takes pairs of points or objects to real numbers and satisfies the following rules:
As an exception, many of the divergences used in statistics are not metrics. Distance between setsThe distances between these three sets do not satisfy the triangle inequality:d ( A , B ) > d ( A , C ) + d ( C , B ) {\displaystyle d(A,B)>d(A,C)+d(C,B)} There are multiple ways of measuring the physical distance between objects that consist of more than one point:
d ( A , B ) = inf x ∈ A , y ∈ B d ( x , y ) . {\displaystyle d(A,B)=\inf _{x\in A,y\in B}d(x,y).} This does not define a metric on the set of such subsets: the distance between overlapping sets is zero, and this distance does not satisfy the triangle inequality for any metric space with two or more points (consider the triple of sets consisting of two distinct singletons and their union).
Related ideasThe word distance is also used for related concepts that are not encompassed by the description "a numerical measurement of how far apart points or objects are". Distance travelledThe distance travelled by an object is the length of a specific path travelled between two points,[6] such as the distance walked while navigating a maze. This can even be a closed distance along a closed curve which starts and ends at the same point, such as a ball thrown straight up, or the Earth when it completes one orbit. This is formalized mathematically as the arc length of the curve. The distance travelled may also be signed: a "forward" distance is positive and a "backward" distance is negative. Circular distance is the distance traveled by a point on the circumference of a wheel, which can be useful to consider when designing vehicles or mechanical gears (see also odometry). The circumference of the wheel is 2π × radius; if the radius is 1, each revolution of the wheel causes a vehicle to travel 2π radians. Displacement and directed distanceDistance along a path compared with displacement. The Euclidean distance is the length of the displacement vector.The displacement in classical physics measures the change in position of an object during an interval of time. While distance is a scalar quantity, or a magnitude, displacement is a vector quantity with both magnitude and direction. In general, the vector measuring the difference between two locations (the relative position) is sometimes called the directed distance.[7] For example, the directed distance from the New York City Main Library flag pole to the Statue of Liberty flag pole has:
Signed distanceIn mathematics and its applications, the signed distance function (or oriented distance function) is the orthogonal distance of a given point x to the boundary of a set Ω in a metric space, with the sign determined by whether or not x is in the interior of Ω. The function has positive values at points x inside Ω, it decreases in value as x approaches the boundary of Ω where the signed distance function is zero, and it takes negative values outside of Ω.[8] However, the alternative convention is also sometimes taken instead (i.e., negative inside Ω and positive outside).[9] See also
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