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**Zamzen** A free falling body has no initial velocity. Its mass is 80kg and the air resistence is proportional to the velocity squared with the proportional constant 0.16kg/m.Let velocity be y m/s and x s. And the question is to put up a differential equation for this.

My attempt at the solution.

y(0)=0 (easy part). Now my thinking about the equation itself goes something like this.

F=ma

a=9.82

F(t) = F-Fr(t) (Fr=Air resistance)

ma(t)=ma- v^2 * 0.16(t)

divide it all by m which is 80

a(t) = 9.82 - 0.002v^2(t)

swapping out v(t) for y and a(t) for dy/dt

dy/dt=9.82 - 0.002y^2

which is correct according to the text book.

My issue is That it seems that i have solved for the accelration and not for the velocity itself. Im thankful if anyone could explain this.