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

MATH102 December 2016

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Question B 03 (a)

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 ${\frac {dv}{dt}}=g-kv$ where $g\approx 10^{7}\mu m/s^{2}$ is the gravitational acceleration, $kv$ is the acceleration due to drag and $k=10^{13}s^{-1}$. (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.) (a) What is the steady state velocity, $v_{ss}$, of the protein? Include units in your answer.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Steady state is when ${\frac {dv}{dt}}=0$ .

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Solution
Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. When ${\frac {dv}{dt}}=0$ we have $g-kv=0$, so $v=v_{ss}={\frac {g}{k}}={\frac {10^{7}\ \mu m/s^{2}}{10^{13}\ s^{-1}}}=\color {blue}10^{-6}\ \mu m/s$ .