# Re: DE word problem

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Posted by Subhotosh Khan on September 03, 2002 at 13:40:05:

In Reply to: Re: DE word problem posted by colin on September 03, 2002 at 13:30:50:

: : : A body with mass m is projected vertically downward with initial velocity v0 in a medium offering resistance proportional to the square root of the magnitude of the velocity. Find the relation between the velocity v and the time t.

: : : Do I solve for v or t here? How can I tell?

: : This is an F=ma problem:

: : 1) Pick a positive direction. How about positive is down.

: : 2) Draw a force diagram mg points down and f sqrt(v) points up.

: : 3) Sum the forces and set equal to ma

: : 4) m g - f sqrt(v) = m a

: : 5) Note that a=(dv)/(dt)

: : 6) rewrite :

: : (dv)/(dt)=g-(f sqrt(v))/m

: : 7) Solve with vo at t=0

: Thank you... In the book, they show the solution solved for t, not v. I'm confused about why they solved for t not v. Was there any clue in the initial problem statement?
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It should not really matter - whether it is t(v) or v(t) - one is inverse of the other.

In this problem, you will find t(v) first because the equation becomes:

dt = dv/(g - k*sqrt(v))

which you can integarte directly to get t(v).

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