Kinematics

Kinematics is a branch of classical mechanics that describes the motion of objects without considering the forces that cause the motion. It analyzes where objects are located, how their positions change over time, and how their velocity and acceleration evolve. The basic quantities are position, displacement, velocity, speed, and acceleration. Position specifies an object’s location in a chosen reference frame; displacement is the change in position. Velocity is the rate of change of position and is a vector; speed is its scalar magnitude. Acceleration is the rate of change of velocity and is also a vector. The choice of reference frame affects measured motion, and kinematic relations are often expressed in vector form.

In one-dimensional motion, position is a function x(t). With constant acceleration a, the standard relations are x = x0 + v0 t + 1/2 a t^2, v = v0 + a t, and v^2 = v0^2 + 2 a (x − x0). In two or three dimensions, position becomes a vector r(t) = r0 + v0 t + (1/2) a t^2, with components x(t), y(t), z(t). Trajectories describe the path followed; projectile motion is a common kinematic problem neglecting air resistance.

Other concepts include uniform motion (a = 0), uniformly accelerated motion, and relative motion between observers in different reference frames. Kinematic analysis often uses graphs of position-time, velocity-time, and acceleration-time.

Kinematics is distinct from kinetics, which studies the forces and torques that cause motion. Applications span physics and engineering problem solving, robotics, computer animation, and biomechanics, where motion is analyzed and predicted based on observed positions and rates of change.