### High School Physics - Kinematics

Displacement $\vec{x(t)}$, Velocity $\vec{v(t)}$, and Acceleration $\vec{a(t)}$: $\lim\limits_{\Delta t\to 0}\frac{\vec{\Delta x}}{\Delta t} = \vec{v} = \int_{t_i}^{t_f}\vec{a}dt$

Uniform Accelerated Motion ($\vec{a}$ has constant magnitude, direction) $\boxed{5-3-2}$

$\displaystyle \vec{\Delta x} = \vec{v_i}\Delta t+\frac{1}{2}\vec{a}(\Delta t)^2 = \vec{v_f}\Delta t-\frac{1}{2}\vec{a}(\Delta t)^2$

$\displaystyle{\vec{v_f^2} = \vec{v_i^2}+2\vec{a}\vec{\Delta{x}}\Leftarrow \begin{cases}\vec{v}_f = \vec{v}_i+\vec{a}\Delta t\\ \vec{\Delta x} = \Big(\frac{\vec{v_i}+\vec{v_f}}{2}\Big) \Delta t\end{cases}}$

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