# Calculate time to go from one point to another point [closed]

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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Hi Arash, and welcome to Physics Stack Exchange! This is a site for conceptual questions about physics, not a reference for basic formulas. Have you tried checking references like a textbook, Wikipedia, or other websites? – David Zaslavsky Sep 18 '12 at 17:34
ok,yes i searched about that but i didnt find anything – Arash Ata Afarin Sep 18 '12 at 17:38
thanks,i edited my question but its still closed! – Arash Ata Afarin Sep 18 '12 at 18:07
Could you clarify what "parameter about effect of decay on ball speed" means? – David Zaslavsky Sep 18 '12 at 18:35

## 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.

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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thanks,can you please say about what is g and k? – Arash Ata Afarin Sep 18 '12 at 18:10
$g$ is acceleration due to gravity, and $\kappa$ is an aerodynamic constant, typically calculated by $\kappa = \frac{1}{2} \rho A C_d$ with $A$ the swept area, $\rho$ the air density, and $C_d$ the coefficient of drag. – ja72 Sep 18 '12 at 18:16
in soccer simulation 2d that is a field of robotic, we do not have gravity.only agent that effect on speed of ball is ball decay and it has a constant value in each cycle – Arash Ata Afarin Sep 18 '12 at 18:22
You will need a simulation to solve this problem then. That's what computers were invented for, literally the first computers were developed by the army math department to create projectile tables. – ja72 Sep 19 '12 at 13:29
You could use the principles in this paper, faculty.kfupm.edu.sa/AE/aymanma/images/… – ja72 Sep 19 '12 at 13:33
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