Time Independent Kinematic Equation

We will work through this several times showing different assumptions. You will notice our assumptions simplify the calculation.

One think to notice right away, we identify final variables with a subscript of “f” and it is tradition for textbook authors to not put any subscript on final variables.

First we assume that the initial velocity is zero and the position is zero at time zero.

v_{f}=v_{0}+at

x_{0}=0

x_{f}=x_{0}+v_{0}t + \dfrac{1}{2}at^{2}

…

with no zero value assumptions, we get x being equal to six terms, but cancellations and combination reduce this to

2a(x_{f}-x_{0})=v^{2} - {v_{0}}^{2}