Formulas for constant acceleration

In physics, particularly kinematics, the formulas for constant acceleration are a set of five equations that describe the motion of a particle that has a constant acceleration. The formulas can be derived from the instantaneous velocity given by the first derivative, and then mathematical integration yields the formulas.

The Formulas

In the following formulas, $v_{f}$ is the final velocity, $v_{i}$ is the initial velocity, $a$ is the acceleration, (which must be constant for the formulas to be valid), $\Delta t$ is the duration of time, and $d$ is the displacement.

1) $v_{f}=v_{i}+a\Delta t$

2) $v_{f}^{2}=v_{i}^{2}+2ad$

3) $d={\frac {1}{2}}(v_{f}+v_{i})\Delta t$

4) $d=v_{i}\Delta t+{\frac {1}{2}}a\Delta t^{2}$

5) $d=v_{f}\Delta t-{\frac {1}{2}}a\Delta t^{2}$