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For this problem $y$ is the variable for the displacement, $v$ is the velocity, $m$ is the mass, $k$ is the constant of proportionality.

The force on the object is the mass times the acceleration: $F=$

$$ my$"$ in terms of $y$ or in terms of the velocity we have $F=m^{\text{'}}{v}^{\text{'}}$

For an object in free fall there are two forces: the force due to gravity $($positive g$)$ and the force due to air resistance, which is proportional to the velocity and acts in the opposite direction. Therefore $F=.$

Putting these two together we get a differential equation for the force acting on an object in free fall in terms of the velocity v :

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