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Define distance and displacement, and distinguish between the two; Solve problems involving distance and displacement
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We can talk about the distance between two points, or we can talk about the distance traveled by an object. Distance is defined to be the magnitude or size of displacement between two positions. Note that the distance between two positions is not the same as the distance traveled between them.
Distance is the length of the path taken by an object whereas displacement is the simply the distance between where the object started and where it ended up. For example, lets say you drive a car. You drive it 5 miles east and then 3 miles west.
28 mar 2024 · In spherical coordinates, a point \(P\) is described by the radius, \(r\), the polar angle \(\theta\), and the azimuthal angle, \(\phi\). The radius is the distance between the point and the origin. The polar angle is the angle with the \(z\) axis that is made by the line from the origin to the point. The azimuthal angle is defined in the same ...
20 lip 2022 · The cylindrical coordinates for a point P P are the three numbers (r,θ, z) ( r, θ, z) (Figure 3.12). The number z z represents the familiar coordinate of the point P P along the z z -axis. The nonnegative number r represents the distance from the z z -axis to the point P P.
It is therefore very easy to do calculations in Cartesian coordinates. For example, the distance Δs Δ s between two points (x1,x2,…,xn) ( x 1, x 2, …, x n) and (x′ 1,x′ 2,…,x′ n) ( x 1 ′, x 2 ′, …, x n ′) can be quickly computed using a general formula for n-dimensions: Δs2 = (x′ 1 −x1)2 +(x′ 2 −x2)2+…+(x′ n ...
We can define alternative, non-Cartesian, coordinate systems for Euclidean space; for instance, cylindrical and spherical coordinate systems are very useful in physics, and they use mixtures of linear or radial distance, and angles, as the numbers to specify points of space.
