Uniform Linear Motion and Uniformly Accelerated Linear Motion

The study of Uniform Rectilinear Motion (URM) and Uniformly Accelerated Rectilinear Motion (UARM) is essential for understanding the fundamentals of kinematics. In URM, velocity remains constant, and position is described by the equation:

$$ x(t) = x_0 + v\,t $$

In UARM, acceleration is constant and is characterized by the equations:

$$ x(t) = x_0 + v_0\,t + \frac{1}{2}a\,t^2 \quad\text{and}\quad v(t) = v_0 + a\,t. $$

These relationships allow for the analysis of position, velocity, and acceleration variations over time and form the basis for understanding physical phenomena involving motion with or without acceleration.