The equation x=1/2(vi+vf)t represents the displacement (or change in position) of an object over a certain period of time. It is often used to calculate the distance an object travels when its initial and final velocities are known.
This equation is derived from the kinematic equations of motion, specifically the equation x=xit+1/2at^2, where x is the displacement, vi is the initial velocity, vf is the final velocity, t is the time, and a is the acceleration. By substituting vi and vf with (vi+vf)/2 (the average velocity), the equation x=1/2(vi+vf)t is obtained.
This equation is most commonly used in situations where an object is moving at a constant acceleration. This can include free fall, projectile motion, and motion with a constant force.
Yes, this equation can be rearranged to solve for any of the variables x, vi, vf, or t, as long as the values for the other variables are known. For example, if the initial velocity, final velocity, and time are known, the equation can be rearranged to solve for displacement (x).
While this equation is useful for calculating displacement in specific situations, it does have some limitations. It assumes that the acceleration is constant and that there are no external forces acting on the object. Additionally, it does not take into account factors such as air resistance or changes in the acceleration of the object.