Equations of motion

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Equations of motion are equations that describe the behavior of a system (e.g., the motion of a particle under the influence of a force) as a function of time.[1] Sometimes the term refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.

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Equations of uniformly accelerated linear motion

The equations that apply to bodies moving linearly (in one dimension) with constant acceleration are often referred to as "SUVAT" equations where the five variables are represented by those letters (s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time); the five letters may be shown in a different order.

The body is considered between two instants in time: one initial point and one current (or final) point. Problems in kinematics may deal with more than two instants, and several applications of the equations are then required. If a is constant, the differential, a dt, may be integrated over an interval from 0 to Δt (Δt = tti), to obtain a linear relationship for velocity. Integration of the velocity yields a quadratic relationship for position at the end of the interval.

where...

and its current state is described by:

Note that each of the equations contains four of the five variables. Thus, in this situation it is sufficient to know three out of the five variables to calculate the remaining two.

Classic version

The equations below (often informally known as the "suvat"[2] equations) are often written in the following form:[3]

By substituting (1) into (2), we can get (3), (4) and (5). (6) can be constructed by rearranging (1).

where

Examples

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