Diferencia entre las páginas «Archivo:F1 GIC PPC doble barra enunciado.png» y «Partícula con movimiento rectilíneo, Noviembre 2012 (G.I.C.)»

${\displaystyle [a\,v]=[C^{2}t^{2}]\Longrightarrow [C^{2}]=\left[{\dfrac {a\,v}{t^{2}}}\right]={\dfrac {L\,T^{-2}\,L\,T^{-1}}{T^{2}}}=L^{2}\,T^{-5}}$

${\displaystyle [C]=L\,T^{-5/2}}$

${\displaystyle a={\dfrac {\mathrm {d} v}{\mathrm {d} t}}}$

${\displaystyle v\,{\dfrac {\mathrm {d} v}{\mathrm {d} t}}={\dfrac {3C^{2}}{2}}\,t^{2}}$

${\displaystyle v\,\mathrm {d} v={\dfrac {3\,C^{2}}{2}}\,t^{2}\,\mathrm {d} t}$

${\displaystyle \int \limits _{v_{0}}^{v(t)}v\,\mathrm {d} v=\int \limits _{0}^{t}{\dfrac {3\,C^{2}}{2}}\,t^{2}\,\mathrm {d} t}$

${\displaystyle v(t)={\sqrt {v_{0}^{2}+C^{2}\,t^{3}}}}$

${\displaystyle v(t)=C\,t^{3/2}}$

${\displaystyle v={\dfrac {\mathrm {d} x}{\mathrm {d} t}}\Longrightarrow \mathrm {d} x=v(t)\,\mathrm {d} t}$

${\displaystyle \int \limits _{0}^{x(t)}\mathrm {d} v=\int \limits _{0}^{t}C\,t^{3/2}\,\mathrm {d} t}$

${\displaystyle x(t)={\dfrac {2\,C}{5}}\,t^{5/2}}$