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

Step-by-step solution

The particle experiences downward gravitational force (mg) and upward resistive force (-kv). The equation of motion is m dv dt = mg - kv . Initially at t=0 , v=0 gives maximum acceleration a₀ = g . As velocity increases, the resistive force increases, reducing the net acceleration. Eventually the particle reaches terminal velocity v_t = mg k when acceleration becomes zero. The velocity-time graph shows an increasing curve starting from origin with decreasing slope, asymptotically approaching the terminal velocity.