Question 8 of 210

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 ($t$)?

ABCD

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Answer: (A)

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.