Question

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.)

Answer 1

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

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

$$mg-kV=ma$$

Where a - acceleration of object

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

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

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