in a 2D football game I want to calculate cycle(time) until ball go from one point to another point.
in this link exist all fomulas that we need for my problem but anyone does not have any parameter that shows the effect of decay on ball speed.
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closed as too localized by David Zaslavsky♦ Sep 18 '12 at 17:33
This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, see the FAQ.
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If you know the acceleration $a(v)$ as a function of speed (as in aerodynamic drag) then $$ \Delta t = \int_{v_1}^{v_2} \frac{1}{a(v)}\,{\rm d}v $$ For example, a free falling body with air resistance has acceleration (positive is up) $$ a(v) = \kappa v^2 - g $$ where $\kappa$ is some constant. The time to reach speed $v$ from standstill is $$ \Delta t = \int_v^0 \frac{1}{\kappa v^2-g}\,{\rm d} v = -\frac{ \ln\left( \frac{\sqrt{g}-\sqrt{\kappa} v}{\sqrt{g}+\sqrt{\kappa} v}\right)}{2 \sqrt{\kappa g}} $$ or the inverse $$ v(t) = \sqrt{\frac{g}{\kappa}} \, \frac{1-{\rm e}^{-\sqrt{\kappa g}\, 2 t}}{1+{\rm e}^{-\sqrt{\kappa g}\, 2 t}} $$ with terminal velocity $$ v(t=\infty) = \sqrt{\frac{g}{\kappa}} $$ |
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