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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 constants. What is the velocity at any time t?

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 constants. What is the velocity at any time t?

Grade:11

4 Answers

Prajwal kr
49 Points
9 years ago

dv/(a-bv)=dt

Integrating both sides we get:

-ln(a-bv)/b=t

=>

v=(a-e-bt)/b

Saurabh Anand
38 Points
9 years ago

v = (a/b) (1-(e-bt))....just integrate it...

vivek kumar
57 Points
9 years ago

integrate it

Pratibha Rani
39 Points
9 years ago

you just need to integrate it

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