Question

de la formula de distancia s=vot+1/2at2 despejar el tiempo

Answer 1

$\[s = {s_0} + {v_0}t + \frac{1}{2}a{t^2}\]$

$\[\frac{1}{2}a{t^2} + {v_0}t + {s_0} - s = 0\]$

$\[t = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\]$

Donde:

$\[\begin{gathered} a = \frac{1}{2}a \hfill \\ b = {v_0} \hfill \\ c = {s_0} - s \hfill \\ \end{gathered} \]$

$\[t = \frac{{ - \left( {{v_0}} \right) \pm \sqrt {{{\left( {{v_0}} \right)}^2} - 4\left( {\frac{1}{2}a} \right)\left( {{s_0} - s} \right)} }}{{2\left( {\frac{1}{2}a} \right)}}\]$

$\[t = \frac{{ - {v_0} \pm \sqrt {{v_0}^2 - 2a\left( {{s_0} - s} \right)} }}{a}\]$

Tomar el signo positivo de la raíz ( un tiempo negativo, carece de sentido).

$\[t = \frac{{ - {v_0} + \sqrt {{v_0}^2 - 2a\left( {{s_0} - s} \right)} }}{a}\]$