Rational reconstruction (mathematics)

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), $\mathrm{\Delta }t$ is the duration of time, and $d$ is the displacement.

1) $v_f=v_i+a\mathrm{\Delta }t$

2) $v_f^2=v_i^2+2ad$

3) $d=\frac{1}{2}(v_f+v_i)\mathrm{\Delta }t$

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

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