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We will model the movement of an object moving through a viscous medium with the following differential equation:
m.dV/dt = mg - kV
where m is the mass of the object,
k is a scaling or proportionality factor that accounts for the area experiencing the viscous force, dimensional formula is MT-1
V is the velocity,
=> integral of [dV/(mg - kV)] limits from 1 to 0.63Vt = integral of [ dt/m ] limits from 0 to T(time constant)
on solving gives T=(m/k)*ln[mg / (mg - 0.63Vt)]
where its dimesnion formula is T
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