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## Homework Statement

Only force acting on body is drag force $$F=kv^a$$ where k is constant, a coefficient bigger than zero and v is velocity. Body is given initial velocity u.

Find a such that body travels infinitely large distance.[/B]

## Homework Equations

$$F=kv^a$$

$$F=m(acceleration)$$

$$acceleration=dv/dt=d^2s/dt^2$$[/B]

## The Attempt at a Solution

Since distance is infinite I think that v should never reach zero.

From $$-m \frac{dv}{dt}=kv^a$$ I found v(t) :

$$v=(u^{-a+1}- \frac{kt}{m}(1-a))^{\frac{1}{-a+1}}$$

Here I looked at cases a<1,a=1,a>1 and im not sure but i think that a=1 is good.

Is this ok?

[/B]

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