- #1

alex_b93

- 13

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## Homework Statement

Particle (Mass = m) falling through a viscous liquid due to gravity.

Experiences a drag force that is proportional to its speed.

Magnitude of drag force .

F = ku = +ve Constant x velocity.

At time t = 0, z = position = 0, initial speed = u_0.

## Homework Equations

Acceleration found to be

du/dt = g - (k/m)u

## The Attempt at a Solution

So to find the velocity this needs to be integrated, the way I attempted to do it was to separate the variables and substitute in

α = mg / k

Meaning

(du/dt) = g(1-u/α)

This lead to the integral

∫(α du/ α-u) = ∫g dt

α∫(1/-u) du = g ∫dt

-α ln (α-u) = gt + c

ln (α-u) = -(gt + c )/α

(α-u) = exp -(gt + c)/α

u = α - exp[-(gt+c)/α]

Would that be correct up to there, because when I carry on to find c and to substitute for α it gets messy, so I'm unsure if I've done it right.

Thanks