(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a ball with mass [itex]m[/itex] is thrown up from the ground with a velocity [itex]v_0[/itex]

the force due to Air resistance is: [itex]F=-bv[/itex]

(there's also gravity)

find the velocity and distance with respect to time

3. The attempt at a solution

I think I got the velocity:

[itex]v=e^{-\frac{b}{m}t}(\frac{m}{b}g+v_0)-\frac{m}{b}g [/itex]

the units are okay and so does t=0 (v=v_{0})

I have a problem with the distance, I integrate:

[itex]x=\int^{t}_{0}vdt=\int^{t}_{0}(e^{-\frac{b}{m}t}(\frac{m}{b}g+v_0)-\frac{m}{b}g) = -e^{-\frac{b}{m}t}(\frac{m}{b}g+v_0)\frac{m}{b}-\frac{m}{b}gt [/itex]

so the units are okay but if t=0 [itex]x=-(\frac{m}{b}g+v_0)\frac{m}{b}-\frac{m}{b}gt[/itex]

and it should be 0 (or so I think)

maybe the constant of integration should be the expression I got?

I'm really confused.

Thanks in advance!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: (Air Resistance) Distance with respect to time

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