Key Equations

Displacement	$Δ x = x_{f} - x_{i}$
Total displacement	$Δ x_{Total} = \sum Δ x_{i}$
Average velocity	$\overset{–}{v} = \frac{Δ x}{Δ t} = \frac{x_{2} - x_{1}}{t_{2} - t_{1}}$
Instantaneous velocity	$v (t) = \frac{d x (t)}{d t}$
Average speed	$Average speed = \overset{–}{s} = \frac{Total distance}{Elapsed time}$
Instantaneous speed	$Instantaneous speed = \| v (t) \|$
Average acceleration	$\overset{–}{a} = \frac{Δ v}{Δ t} = \frac{v_{f} - v_{0}}{t_{f} - t_{0}}$
Instantaneous acceleration	$a (t) = \frac{d v (t)}{d t}$
Position from average velocity	$x = x_{0} + \overset{–}{v} t$
Average velocity (for constant acceleration)	$\overset{–}{v} = \frac{v_{0} + v}{2}$
Velocity from acceleration	$v = v_{0} + a t (constant a)$
Position from velocity and acceleration	$x = x_{0} + v_{0} t + \frac{1}{2} a t^{2} (constant a)$
Velocity from distance	$v^{2} = v_{0}^{2} + 2 a (x - x_{0}) (constant a)$
Velocity of free fall	$v = v_{0} - g t (positive upward)$
Height of free fall	$y = y_{0} + v_{0} t - \frac{1}{2} g t^{2}$
Velocity of free fall from height	$v^{2} = v_{0}^{2} - 2 g (y - y_{0})$
Velocity from acceleration	$v (t) = \int a (t) d t + C_{1}$
Position from velocity	$x (t) = \int v (t) d t + C_{2}$