\begin{align*} v_x&=u_x+a_xt\\ \Delta x&=\left(\dfrac{u_x+v_x}{2}\right)t\\ \Delta x&=u_xt+\dfrac{1}{2}a_xt^2\\ v_x^2&=u_x^2+2a_x\Delta x \end{align*}

\[\sum \vec{F}=m\vec{a}\]

\[f_{\text{s}}\leq\mu_\text{s}N\]

\[f_\text{k}=\mu_\text{k}N\]

\[F_\text{G}=\dfrac{Gm_1m_2}{r^2}\]

\[\vec{W}=m\vec{g}\]

\[\sum \vec{F}=0\]

\[M=Fl=Fr\sin\theta\]

\[\sum M=0\]

\[W=\vec{F}\cdot\Delta \vec{x}=F_x\Delta x\cos\theta\]

\[W_{\text{gravity}}=-mg\Delta h\]

\[P_{\text{av}}=\dfrac{W}{\Delta t}\]

\[E_\text{k}=\dfrac{1}{2}mv^2\]

\[W=E_\mathrm{k_f}-E_\mathrm{k_i}\]

\[E_\text{p}=mgh\]

\[F_\text{s}=-kx\]

\[E_\mathrm{p_s}=\dfrac{1}{2}kx^2\]

\[\text{Efficiency}=\dfrac{W_{\text{out}}}{W_{\text{in}}}\times100\%\]

\[\text{M.A.}=\dfrac{F_\text{out}}{F_\text{in}}=\dfrac{s_\text{in}}{s_\text{out}}\]

\[\vec{p}=m\vec{v}\]

\[\sum \vec{F}=\dfrac{\Delta \vec{p}}{\Delta t}\]

\[\vec{I}=\left(\sum \vec{F} \right) \Delta t=\Delta \vec{p}\]

\[\vec{p}_\text{i}=\vec{p}_\text{f}\]