Physics

Motion Equations Velocity Average Velocity $$ \vec{v}=\frac{\Delta \vec{r}}{\Delta t} $$ $$ \vec{v}=\frac{\Delta \vec{r}}{\Delta t} $$ $$ unit: \frac{m}{s} $$ Instant Velocity $$ \vec{v}=\frac{d\vec{r}}{dt} $$ $$ \vec{v}=\frac{d\vec{r}}{dt} $$ $$ unit: \frac{m}{s} $$ Acceleration Average Acceleration $$ \vec{a}=\frac{\Delta \vec{v}}{\Delta t} $$ $$ \vec{a}=\frac{\Delta \vec{v}}{\Delta t} $$ Instant Acceleration $$ \vec{a}=\frac{d\vec{v}}{dt} $$ $$ \vec{a}=\frac{d\vec{v}}{dt} $$ $$ unit: \frac{m}{s^{2}} $$ Non-Uniform Motion Velocity $$ v=\frac{ds}{dt} $$ $$ v=\frac{ds}{dt} $$ $$ \int_{s_i}^{s_f}ds=\int_{t_i}^{t_f}vdt $$ $$ \int_{s_i}^{s_f}ds=\int_{t_i}^{t_f}vdt $$ $$ s_f-s_i=\Delta s=\int_{t_i}^{t_f}vdt $$ $$ s_f-s_i=\Delta s=\int_{t_i}^{t_f}vdt $$ $$ s_f=s_it\int_{t_i}^{t_f}vdt $$ $$ s_f=s_it\int_{t_i}^{t_f}vdt $$ Acceleration $$ a=\frac{dv}{dt} $$ $$ a=\frac{dv}{dt} $$ $$ \int_{t_i}^{t_f}adt=\int_{v_i}^{v_f}dv $$ $$ \int_{t_i}^{t_f}adt=\int_{v_i}^{v_f}dv $$ $$ v_f-v_i=\int_{t_i}^{t_f}adt $$ $$ v_f-v_i=\int_{t_i}^{t_f}adt $$ $$ v_f=v_i+\int_{t_i}^{t_f}adt $$ $$ v_f=v_i+\int_{t_i}^{t_f}adt $$ Vectors $$ \vec{A}=\vec{A_x}+\vec{A_y} $$ $$ \vec{A}=\vec{A_x}+\vec{A_y} $$ Unit Vectors $$ \hat{i}\parallel x $$ $$ \hat{j}\parallel y $$ $$ \hat{i}\parallel x $$ $$ \hat{j}\parallel y $$ $$ \vec{A_x}=A_x\hat{i}, $$ $$ \vec{A_y}=A_y\hat{j} $$ $$ \vec{A_x}=A_x\hat{i}, $$ $$ \vec{A_y}=A_y\hat{j} $$ $$ \vec{A}=A_x\hat{i}+A_y\hat{j} $$ $$ \vec{A}=A_x\vec{i}+A_y\vec{j} $$ Multiplication Scaler $$ \beta\vec{A}=\beta(A_x\hat{i}+A_y\hat{j}) $$ $$ \beta\vec{A}=\beta(A_x\hat{i}+A_y\hat{j}) $$ Dot Product $$ \vec{A}\cdot\vec{B}= $$ Cross Product $$ \vec{A}\times\vec{B}=\vec{C} $$ $$ \vec{A}\times\vec{B}=\vec{C} $$ $$ |\vec{A}\times\vec{B}|=|\vec{A}||\vec{B}|sin(\alpha)=|\vec{C}| $$ $$ |\vec{A}\times\vec{B}|=|\vec{A}||\vec{B}|sin(\alpha)=|\vec{C}| $$ \(\odot\) : out of plane \(\otimes\) : into plane...