Calculating Terminal Velocity of a Free Falling Body with Air Resistance

[aeb2335]

Homework Statement

Given: effects of drag for a free falling body are a= 9.81[1-(v^2)*10^-4] m/s^2
V0 = 0 m/s and the falling body is very very high

Find: the velocity after 5 seconds and the bodies terminal velocity as t -> infinity

Homework Equations

∫dv = ∫a dt

The Attempt at a Solution

∫ 1/(1-(v^2)*10^(-4)) dv = ∫ 9.81 dt where t goes from 0 to 5

When I integrate this I get

5*10^(-4) * ln( abs( v+1) / abs( v -1)) - 5*10^(-4) * ln( abs(1) / abs( 1)) = 9.81 m/s^2 * 5s

For some reason I don't think this is right and if it is how do you solve it?

thanks

 

[haruspex]

You have dv/dt = 9.81[1-(v^2)*10^-4].
Can you rearrange that as t = ∫ f(v) dv?