# Kinematic Equations – III

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Physik
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JoVE Core Physik
Kinematic Equations – III

### Nächstes Video3.10: Kinematic Equations: Problem Solving

The first and the second kinematic equations both have time as a variable.

The third equation is independent of time and includes the relationship between the variables displacement, velocity, and constant acceleration.

The first equation of kinematics is rearranged to obtain an expression for time. Further, this time expression is substituted into the second equation of kinematics. Shift the term x0 to the left side and multiply both sides by 2ax. Simplifying it further gives an expression for the final velocity squared equal to the initial velocity squared plus two times the acceleration multiplied by the difference between the final and initial distance. This is the third kinematic equation.

The fourth kinematic equation does not involve constant x-acceleration and can be obtained by equating the two expressions for the average velocity introduced earlier. Both sides are then multiplied by time t. This gives a relationship stating that the difference between final and initial distance is equal to the average of the velocity at initial and final time multiplied by time t.

## 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.