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In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. [1] It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory.
The first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1 2 = 4.9 m. After two seconds it will have fallen 1/2 × 9.8 × 2 2 = 19.6 m; and so on. On the other hand, the penultimate equation becomes grossly inaccurate at great distances.
Absement changes as an object remains displaced and stays constant as the object resides at the initial position. It is the first time-integral of the displacement [3] [4] (i.e. absement is the area under a displacement vs. time graph), so the displacement is the rate of change (first time-derivative) of the absement.
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
Position, when thought of as a displacement from an origin point, is a vector: a quantity with both magnitude and direction. [9]: 1 Velocity and acceleration are vector quantities as well. The mathematical tools of vector algebra provide the means to describe motion in two, three or more dimensions.
The differential equation above takes the form of 1D heat equation. The one-dimensional PDF below is the Green's function of heat equation (also known as Heat kernel in mathematics): P ( x , t ) = 1 4 π D t exp ( − ( x − x 0 ) 2 4 D t ) . {\displaystyle P(x,t)={\frac {1}{\sqrt {4\pi Dt}}}\exp \left(-{\frac {(x-x_{0})^{2}}{4Dt}}\right).}
Its length represents the distance in relation to an arbitrary reference origin O, and its direction represents the angular orientation with respect to given reference axes. Usually denoted x, r, or s, it corresponds to the straight line segment from O to P. In other words, it is the displacement or translation that maps the origin to P: [1]
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
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