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motion of bodies
Equations of motion
Equations of motion
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. 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 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, a differential, a dt, may be integrated over an interval from 0 to
), to obtain a linear
relationship for velocity. Integration of the velocity yields a quadratic relationship for position at the end of the
is the body's initial velocity
is the body's initial position
and its current state is described by:
, The velocity at the end of the interval
, the position at the end of the interval (displacement)
, the time interval between the initial and current states
, the constant acceleration, or in the case of bodies moving under the influence of gravity, g.
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.
The above equations are often written in the following form: