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, x velocity, and constant x 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 x 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 x velocity at initial and final time multiplied by time t.