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NTA Abhyas JEE Main2020PhysicsMotion in One DimensionPractice

The motion of a body falling from rest in a resistive medium is described by the equation d v d t = a - b v , where a and b are constants. The velocity at any time t is

Options

  1. Aa ( 1 - b 2 t )
  2. Ba b ( 1 - e - b t )
  3. Ca b e - t
  4. Da b 2 ( 1 - t )

Correct answer

B. a b ( 1 - e - b t )

Step-by-step solution

d v d t = a - b v or ∫ 0 v d v a - b v = ∫ 0 t d t or - 1 b l o g a - b v 0 v = t or a - b v a = e - b t or a - b a v = e - b t v = a b ( 1 - e - b t )

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