3.9 : Kinematic Equations - III

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.

Using the kinematic equations, descriptive information about an object's motion can be obtained. The process of developing kinematics also provides a glimpse of a general approach to problem-solving that produces both correct answers and insights into physical relationships. These equations and the associated problem-solving strategies are helpful only when the acceleration is constant; if the acceleration of the object is not constant, then a different approach to solve for the object's dynamics is required.

The applicability of the kinematic equations is not limited to one-dimensional motion. These equations can be generalized to the higher dimensions, provided the acceleration of the object is constant. Similarly, these equations can also be generalized to rotational motion using appropriate physical quantities that describe the rotational motion of the object, as long as the angular acceleration of the object is constant.

This text is adapted from Openstax, University Physics Volume 1, Section 3.4: Motion with Constant Acceleration.