Key Equations

Displacement	$\text{Δ}x=x_{\text{f}}-x_{\text{i}}$
Total displacement	$\text{Δ}{x}_{\text{Total}}={\displaystyle \sum \text{Δ}{x}_{\text{i}}}$
Average velocity	$\stackrel{\text{–}}{v}=\frac{\text{Δ}x}{\text{Δ}t}=\frac{x_2-x_1}{t_2-t_1}$
Instantaneous velocity	$v(t)=\frac{dx(t)}{dt}$
Average speed	$\text{Average speed}=\stackrel{\text{–}}{s}=\frac{\text{Total distance}}{\text{Elapsed time}}$
Instantaneous speed	$\text{Instantaneous speed}=\left|v(t)\right|$
Average acceleration	$\stackrel{\text{–}}{a}=\frac{\text{Δ}v}{\text{Δ}t}=\frac{v_f-v_0}{t_f-t_0}$
Instantaneous acceleration	$a(t)=\frac{dv(t)}{dt}$
Position from average velocity	$x=x_0+\stackrel{\text{–}}{v}t$
Average velocity (for constant acceleration)	$\stackrel{\text{–}}{v}=\frac{v_0+v}{2}$
Velocity from acceleration	$v=v_0+at(\text{constant}a\text{)}$
Position from velocity and acceleration	$x=x_0+v_{0}t+\frac{1}{2}a{t}^2(\text{constant}a\text{)}$
Velocity from distance	$v^2=v_0^2+2a\left(x-x_0\right)(\text{constant}a\text{)}$
Velocity of free fall	$v=v_0-gt\text{(positive upward)}$
Height of free fall	$y=y_0+v_{0}t-\frac{1}{2}g{t}^2$
Velocity of free fall from height	$v^2=v_0^2-2g(y-y_0)$
Velocity from acceleration	$v(t)={\displaystyle \int a(t)dt+C_1}$
Position from velocity	$x(t)={\displaystyle \int v(t)dt+C_2}$