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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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An object falling from rest in air is subject not only to the gravitational force but also to air resistance. Assume that the air resistance is proportional to the velocity with constant of proportionality as k(>0)k(>0) and acts in a direction opposite to motion (g=9.8 m/s2)\left(g=9.8 \mathrm{~m} / \mathrm{s}^2\right). Then velocity at time t=1/kt=1 / k is
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Correct option: A
9.8k(1−e−1)\frac{9.8}{k}\left(1-e^{-1}\right)
Option A (9.8k(1−e−1)\frac{9.8}{k}(1-e^{-1})) is correct because it represents the velocity of the object at time t=1/k, derived by solving the differential equation considering gravity and air resistance.

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