Terminal velocity approach in falling with air resistance

Steps:

• Identify forces: gravitational force mg downward, air resistance kv or kv² upward.
• Net force: ma = mg - kv² (for quadratic drag, common case).
• Solve differential equation: dv/dt = g(1 - (v/vt)²), where vt = √(mg/k).
• Integrate: v(t) = vt tanh(gt/vt), yielding asymptotic v-t graph.

Why A is correct:

• A depicts velocity increasing toward a constant terminal value, matching v = vt tanh(gt/vt) formula for quadratic drag.

Why the others are wrong:

• B shows linear increase, ignoring drag's balancing effect.
• C shows constant velocity from start, neglecting initial acceleration.
• D shows decreasing velocity, contradicting downward fall.

Not enough information on exact P and Q, but assuming standard v-t plot.

Final answer: A