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July 23, 2014

July 23, 2014

Posted by **Joe** on Tuesday, September 8, 2009 at 2:42am.

a=dv/dt=g-kv where k is constnat

Derive a formula for the velocity of the body as a function of time assuming it starts from rest (v=0 at t=0)

v=?

- calc -
**drwls**, Tuesday, September 8, 2009 at 3:01amIntegral of dv/(g - kv) = integral of dt

Integrate both sides, from time from 0 to t; and v from 0 to v, for an equation for t in terms of v. Then invert the equation for v(t)

- calc -
**Joe**, Tuesday, September 8, 2009 at 3:29amIt would be great to see how this is done. The prof's way of doing it is way confusing and intricate and I just started learning integrals.

- calc -
**MathMate**, Tuesday, September 8, 2009 at 8:08amThis is why you'd need to do exercises in integration.

To give you a hint,

∫dv/(g-kv) = -log(g-kv)/k

This could be inferred from standard integrals:

∫dx/(a+bx) = (1/b)log(a+bx)

- calc -
**bobpursley**, Tuesday, September 8, 2009 at 9:15amI agree. I suspect the Prof's method is confusing because you dont understand it....you learn by experience spaced over time. There is no substitute in calculus for hump, grunt, and strain...that is, practice, trial and error.

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