A $320-$lb object is released from rest $500$ ft above the ground and allowed to fall under the influence of gravity. Assuming that the force in pounds due to air resistance is $-20$ v $,$ where v is the velocity of the object in $\backslash (\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$sec$\}\backslash ),$ determine the equation of motion of the object. When will the object hit the ground? Assume that the acceleration due to gravity is $\backslash (32\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$sec$\}^\{2\}\backslash )$ and let $\backslash ($ x$($t$)\backslash )$ represent the distance the object has fallen in t seconds.

Determine the equation of motion of the object.

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x$($t$)=$

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