- #1

Decypher

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Find the displacement and velocity of a particle undergoing vertical motion in a medium having a retarding force proportional to the velocity.

F = m(dv/dt) = -mg-kmv

dv/(kv + g) = -dt

(1/k)ln(kv + g) = -t + c

kv + g = e^(-kt+kc)

v = (dz/dt) = (-g/k) + ((k(Vo) + g)/k)e^(-kt)

I don't see how the e^(-kt + kc) is turning into ((k(Vo) + g)/k

I know a property of exponents allows you to separate the exponents powers when they are being added, then each one becomes the power of an exponent which is where e^-kt comes from, but I am not sure about where the other half of the exponent goes.