Caida Libre.pdf
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𝑚𝑎 = 𝑚𝑔 − 𝑘𝑣 𝑚
𝑑𝑣 = 𝑚𝑔 − 𝑘𝑣 𝑑𝑡
𝑑𝑣 𝑘𝑣 =𝑔− 𝑑𝑡 𝑚 𝑑𝑣 = (𝑔 − ∫
𝑑𝑣 𝑘𝑣 𝑚
(𝑔− )
𝑘𝑣 ) 𝑑𝑡 𝑚
= ∫ 𝑑𝑡 𝑢 = 𝑔 −
𝑚
− 𝑘 ∗ ln (𝑔 − ln (𝑔 − (𝑔 −
𝑘𝑣 ) 𝑚
𝑘𝑣 𝑚
𝑚∗𝑑𝑢 𝑘
∫
−𝑚 𝑘
=𝑡+𝐶
𝑘𝑣 𝑘𝑡 )=− +𝑄 𝑚 𝑚
𝑘𝑡 𝑘𝑣 ) = 𝑒−𝑚 ∗ 𝑄 𝑚 𝑘𝑡
𝑣 = (𝑒 − 𝑚 ∗ 𝑄 − 𝑔) ∗ − 𝑘𝑡
𝑣=
𝑚 (𝑔 𝑘
𝒗=
𝒌𝒕 𝒎 ∗ 𝒈(𝟏 − 𝒆− 𝒎 ) 𝒌
− 𝑒 −𝑚 ∗ 𝑄)
𝑚 𝑘 con condiciones iniciales v = 0 y t = 0 Q = g
𝑘𝑡 𝑑𝑒 𝑚 = ∗ 𝑔(1 − 𝑒 − 𝑚 ) 𝑑𝑡 𝑘
∫ 𝑑𝑒 = 𝒆=
𝑘
𝑑𝑢 = − 𝑚 𝑑𝑥𝑑𝑥 = −
𝑘𝑡 𝑚 ∗ 𝑔 ∫(1 − 𝑒 − 𝑚 )𝑑𝑡 𝑘
𝒎 𝒎 𝒌𝒕 ∗ 𝒈(𝒕 + 𝒆− 𝒎 ) 𝒌 𝒌
∗
𝑑𝑢 𝑢
𝑑𝑣 = 𝑚𝑔 − 𝑘𝑣 𝑑𝑡
𝑑𝑣 𝑘𝑣 =𝑔− 𝑑𝑡 𝑚 𝑑𝑣 = (𝑔 − ∫
𝑑𝑣 𝑘𝑣 𝑚
(𝑔− )
𝑘𝑣 ) 𝑑𝑡 𝑚
= ∫ 𝑑𝑡 𝑢 = 𝑔 −
𝑚
− 𝑘 ∗ ln (𝑔 − ln (𝑔 − (𝑔 −
𝑘𝑣 ) 𝑚
𝑘𝑣 𝑚
𝑚∗𝑑𝑢 𝑘
∫
−𝑚 𝑘
=𝑡+𝐶
𝑘𝑣 𝑘𝑡 )=− +𝑄 𝑚 𝑚
𝑘𝑡 𝑘𝑣 ) = 𝑒−𝑚 ∗ 𝑄 𝑚 𝑘𝑡
𝑣 = (𝑒 − 𝑚 ∗ 𝑄 − 𝑔) ∗ − 𝑘𝑡
𝑣=
𝑚 (𝑔 𝑘
𝒗=
𝒌𝒕 𝒎 ∗ 𝒈(𝟏 − 𝒆− 𝒎 ) 𝒌
− 𝑒 −𝑚 ∗ 𝑄)
𝑚 𝑘 con condiciones iniciales v = 0 y t = 0 Q = g
𝑘𝑡 𝑑𝑒 𝑚 = ∗ 𝑔(1 − 𝑒 − 𝑚 ) 𝑑𝑡 𝑘
∫ 𝑑𝑒 = 𝒆=
𝑘
𝑑𝑢 = − 𝑚 𝑑𝑥𝑑𝑥 = −
𝑘𝑡 𝑚 ∗ 𝑔 ∫(1 − 𝑒 − 𝑚 )𝑑𝑡 𝑘
𝒎 𝒎 𝒌𝒕 ∗ 𝒈(𝒕 + 𝒆− 𝒎 ) 𝒌 𝒌
∗
𝑑𝑢 𝑢
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