A particle of mass m falls from rest through a resistive medium...

The particle experiences downward gravitational force (mg) and upward resistive force (-kv).
The equation of motion is $m\frac{dv}{dt} = mg - kv$.
Initially at $t=0$, $v=0$ gives maximum acceleration $a_0 = g$.
As velocity increases, the resistive force increases, reducing the net acceleration.
Eventually the particle reaches terminal velocity $v_t = \frac{mg}{k}$ when acceleration becomes zero.
The velocity-time graph shows an increasing curve starting from origin with decreasing slope, asymptotically approaching the terminal velocity.
This behavior matches option (1), which displays a curve starting at (0,0) with steep initial slope that gradually flattens.