Answer to Question #96487 in Mechanics | Relativity for Ralph Ruskin Abella

Question #96487
The object of mass m shown above is dropped from rest near Earth’s surface and experiences a resistive force of magnitude kv , where v is the speed of the object and k is a constant. Which of the following expressions can be used to find v as a function of time t ? (Assume that the direction of the gravitational force is positive.)
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Expert's answer
2019-11-06T09:20:48-0500
V=m(g+Vo/t)k+m/tV = \frac{m(g+V_{o} /t)}{k+m/t}


Where V - speed of object, m - mass of object, Vo -initial speed of object, t - time,


mgkV=mamg-kV=ma

Where a - acceleration of object


a=VVota= \frac{V-V_{o}}{t}

mg=kV+m(VVot)mg = kV + m(\frac{V-V_{o}}{t})

V=m(g+Vo/t)k+m/tV = \frac{m(g+V_{o} /t)}{k+m/t}


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