This is not a homework problem, just an idea I had.(adsbygoogle = window.adsbygoogle || []).push({});

If we have a sphere which is being accelerated in space by a force [tex]\vec{F}[/tex] and we take the drag into account, what would the displacement be after t seconds? If the drag force is [tex]\vec{D}=-c_1v-c_2v^2[/tex], then the acceleration would be [tex]\vec{a}=\frac{\vec{F}+\vec{D}}{m} \,,\, a=\frac{F-c_1v-c_2v^2}{m}[/tex] such that the displacement [tex]s=\frac{1}{2}\left(\frac{F-c_1v-c_2v^2}{m}\right)t^2[/tex]. Is this correct? Could someone help me solve this differential equation, if it has a solution?

Thanks for any help.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Displacement with Air Drag

**Physics Forums | Science Articles, Homework Help, Discussion**