The ;motion of a body

Discussion Forum : Physics

Question -

The ;motion of a body falling from rest in a resisting medium is described by the equation `(dv)/(dt) = a - bv`. Where a and b are constant . The velocity at any time t is .

Options:

A . `a(1 - b^(2t))`

B . `a/b (1 - e^-(bt))`

C . `abc^-1`

D . `ab^2(1 - t)`

Answer: Option B

`(dv)/(dt) = a - bv`

or `int_0^v (dv)/(a - bv) = int_0^1 dt`

or ` - 1/2 [log(a - bv)]_0^v = t`

or `((a - bv)/(a)) = e^-(bt)`

or `1 - b/a v = e^-(bt)`1

`:.` ` v = a/b (1 - e^-(bt))`

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