so i got a block with mass=m traveling on an oiled surface. the block suffers a viscous resistance given:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] F(v)= -cv^{3/2} [/tex]

the initial speed of the block is [tex] v_{o} [/tex] at x=0, i have to show that the block cannot travel farther than [tex] 2mv_{o}^{1/2} /c [/tex]

so far i have;

[tex] ma=-cv^{3/2} [/tex]

[tex] m \frac{dv}{dx} \frac{dx}{dt} = -cv^{3/2} [/tex]

[tex] mvdv=-cv^{3/2} dx [/tex]

[tex] dx= \frac {mvdv}{cv^{3/2}} [/tex]

where should i go from here?

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# Horizontal motion with quadratic resistance

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