Mecánica:Desarrollo 1

$(1) v = \frac{d r}{d t} .$ | Definición de Velocidad

$\begin{matrix} (2 a) & a & = & \frac{d v}{d t} = c t e . \\ (2 b) & a & = & \frac{d^{2} r}{d t^{2}} = c t e . \end{matrix} .$ | Definición de Aceleración

$(I) v = \int a d t = a t + v_{0} .$ | Integrando (2a)

$(I I) r = \int \int a d t^{2} = \frac{1}{2} a t^{2} + v_{0} t + r_{0} .$ | Integrando (2b)

$(I I I) a = \frac{v - v_{0}}{t} d e (I)$

$\begin{matrix} (I V) r & = & \frac{1}{2} \frac{v - v_{0}}{t} t^{2} + v_{0} t + r_{0} & d e (I I) y (I I I) \\ = & \frac{1}{2} (v - v_{0}) t + v_{0} t + r_{0} \\ = & \frac{1}{2} (v + v_{0}) t + r_{0} \end{matrix}$

$(V) r - r_{0} = \frac{1}{2} (v + v_{0}) t d e (I V)$

$(V I) 2 (r - r_{0}) = (v + v_{0}) t d e (V) .$ | C.q.d.

$(V I I) t = \frac{v - v_{0}}{a} d e (I)$

$(V I I I) r = \frac{1}{2} a {(\frac{v - v_{0}}{a})}^{2} + v_{0} \frac{v - v_{0}}{a} + r_{0} d e (I I) y (V I I)$

$(I X) r - r_{0} = \frac{1}{2} a {(\frac{v - v_{0}}{a})}^{2} + v_{0} \frac{v - v_{0}}{a} d e (V I I I)$

$\begin{matrix} (X) 2 a (r - r_{0}) & = & (v - v_{0})^{2} + 2 v_{0} (v - v_{0}) & d e (I X) \\ = & (v - v_{0}) [(v - v_{0}) + 2 v_{0}] \\ = & (v - v_{0}) (v + v_{0}) \end{matrix}$

$(X I) 2 a (r - r_{0}) = v^{2} - {v_{0}}^{2} d e (X) .$ | C.q.d.

Mecánica:Desarrollo 1

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