# Science:Math Exam Resources/Courses/MATH102/December 2016/Question B 03 (c)

MATH102 December 2016
Other MATH102 Exams

### Question B 03 (c)

The velocity of a protein inside a cell starting at the top and falling under the force of gravity is given by the differential equation

${\displaystyle {\frac {dv}{dt}}=g-kv}$

where ${\displaystyle g\approx 10^{7}\mu m/s^{2}}$ is the gravitational acceleration, ${\displaystyle kv}$ is the acceleration due to drag and ${\displaystyle k=10^{13}s^{-1}}$.

(Note that this model ignores diffusion of the protein which makes it a really bad model but we’re exploring what gravity alone would do to a protein.)

(c) If the protein is initially at rest at the top of the cell, how long does it take for the protein to reach a velocity of ${\displaystyle (1-e^{-2})v_{ss}}$ (roughly 85% of the way to steady state)? You do not have to solve the equation but instead simply state the solution.

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