\begin{equation} \Delta x = x_2 - x_1 \tag{3.1} \end{equation} \begin{equation} v_{avg} = \frac{x_2 - x_1}{t_2 - t_1} = \frac{\Delta x}{\Delta t} \tag{3.2} \end{equation} \begin{equation} v_{inst} = \lim_{\Delta t\to 0} \frac{\Delta x}{ \Delta t} = \frac{dx}{dt} \tag{3.3} \end{equation} \begin{equation} a_{avg} = \frac{v_2 - v_1}{t_2 - t_1} = \frac{\Delta v}{\Delta t} \tag{3.4} \end{equation} \begin{equation} a_{inst} = \lim_{\Delta t\to 0} \frac{\Delta v}{ \Delta t} = \frac{dv}{dt} \tag{3.5} \end{equation} \begin{equation} a_{inst} = \frac{dv}{dt} = \frac{d}{dt} \left( \frac{dx}{dt} \right) = \frac{d^2 x}{dt^2} \tag{3.6} \end{equation} \begin{equation} x = x_{0} + vt \tag{3.7} \end{equation} \begin{equation} v = v_{0} + at \tag{3.8} \end{equation} \begin{equation} v_{avg} = \frac{v_0 + v_f}{2} \tag{3.9} \end{equation} \begin{equation} x = x_0 + v_0 t + \frac{1}{2} a t^2 \tag{3.10} \end{equation} \begin{equation} v^2 = v_0^2 + 2a \Delta x \tag{3.11} \end{equation} \begin{equation} \Delta x = \frac{v_0 + v}{2} t \tag{3.12} \end{equation} \begin{equation} v_2 - v_1 = \int_{v_1}^{v_2} dv_x = \int_{t_1}^{t_2} a_x dt \tag{3.13} \end{equation} \begin{equation} x_2 - x_1 = \int_{x_1}^{x_2} dx = \int_{t_1}^{t_2} v_x dt \tag{3.14} \end{equation} \begin{equation} v = v_0 + \int_{0}^{t} a \, dt \tag{3.15} \end{equation} \begin{equation} x = x_0 + \int_{0}^{t} v_x \, dt \tag{3.16} \end{equation}
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