The motion of an object in one dimension can be described using a group of five equations that we call the Big Five. They work in cases where acceleration is uniform.
| Name of Equation | Equation | Missing Variable |
| $\mathrm{Big\ Five\ \#1:}$ | $\Delta x=\displaystyle \frac{1}{2}\left(v_0+v\right)t$ | $a$ |
| $\mathrm{Big\ Five\ \#2:}$ | $v=v_0+at$ | $x$ |
| $\mathrm{Big\ Five\ \#3:}$ | $x=x_0+v_0t+\displaystyle \frac{1}{2}at^2$ | $v$ |
| $\mathrm{Big\ Five\ \#4:}$ | $x=x_0+vt-\displaystyle \frac{1}{2}at^2$ | $v_0$ |
| $\mathrm{Big\ Five\ \#5:}$ | $v^2=v^2_0+2a(x-x_0)$ | $t$ |
Each of the Big Five equations is missing one of the five kinematic quantities. To decide which equation to use when solving a problem, determine which of the kinematic quantities is missing from the problem that is, which quantity is neither given nor asked for - and then use the equation that doesn’t contain that variable. A good strategy is to make a list of your “knowns” and your “unknowns.” For example, if the problem never mentions the final velocity - $v$ is neither given nor asked for - the equation that will work is the one that’s missing v. That’s Big Five #3.
Big Five #1 and #2 are simply the definitions of $\overline{v}$ and $\overline{a}$ written in forms that don’t involve fractions. The other Big Five equations can be derived from these two definitions and the equation $\overline{v}=\displaystyle \frac{1}{2}(v_0+v)$ by using a bit of algebra.