Unaccelerated

Unaccelerated is a term used in physics to describe motion or a reference frame in which acceleration is zero. In kinematics, acceleration a is the time derivative of velocity v: a = dv/dt. An unaccelerated motion satisfies a = 0, so velocity remains constant in time.

As a consequence, the position evolves linearly: r(t) = r0 + v0 t. In one dimension, this reduces to x(t) = x0 + v0 t. In a Euclidean, flat-space setting observed from an inertial frame, the path is a straight line. In curvilinear coordinates or noninertial frames, apparent motion can be more complex even if the body has zero proper acceleration.

In Newtonian mechanics, an unaccelerated reference frame is often taken to be an inertial frame: a frame in which Newton’s laws hold without fictitious forces. In special relativity, inertial frames are related by constant-velocity transformations; these frames are unaccelerated relative to one another. Accelerated frames—those undergoing nonuniform motion or forces such as gravity—exhibit fictitious forces or time-dependent effects.

Examples of unaccelerated motion include a car moving at constant speed on a straight road, or a spacecraft coasting with constant velocity in deep space. By contrast, turning, speeding up, or slowing down constitutes acceleration. In everyday contexts, the term is most common in discussions of motion and reference frames, where zero acceleration implies uniform, straight-line motion in an appropriate inertial frame.