- #1
hastings
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Homework Statement
An object with mass m=0.1 kg is thrown with an initial speed v0=20m/s in a viscous matter which opposes its motus with a resistance force of F=-Bv (v is the speed and B=2kg/s). Find the distance this object has covered in the viscous matter. Leave aside gravity force.
Homework Equations
F=m*a
The Attempt at a Solution
I tried this way
[tex]\vec F=-\beta \vec v=m \cdot a[/tex]
[tex]\frac{-\beta \vec v}{m}= a= \frac{dv}{dt}=\frac{ds}{d^2t}[/tex]
[tex]\frac{-\beta \vec v}{m} d^2t=ds [/tex]
[tex]\int{\frac{-\beta \vec v}{m} }d^2t=\int ds [/tex]
[tex]\int{\frac{-\beta \vec v}{m} } \cdot t dt=s[/tex]
[tex]\displaystyle{-\frac{1}{2}} \frac{\beta v }{m}t^2+K=s[/tex]
How to continue? Is it right till this point?