A particle of mass m falls from rest through a resistive medium having resistive force, F = -kv, where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time (t) ?
Options

Question

A particle of mass m falls from rest through a resistive medium having resistive force, F = -kv, where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time (t) ?

Options

G1 Physics · Accepted Answer

Take downward as positive. The forces on the falling particle are mg downward and kv upward. Therefore, m dv/dt = mg-kv. Rearrange: dv/(mg-kv) = dt/m. With v=0 at t=0, integration gives v(t) = (mg/k) [1-exp(-kt/m)]. Thus the velocity starts from zero, increases rapidly at first, and approaches the terminal velocity v(T) = mg/k asymptotically. This shape corresponds to graph shown in option (2). Correct option: B.