The motion of a body falling from rest in a resistive medium is described by the equation $\frac{dv}{dt}=a-bv,$ where $a$ and $b$ are constants. The velocity at any time $t$ is

• A

  $a(1-b^{2t})$
• Correct answer
  B

  $\frac{a}{b}(1-e^{-bt})$
• C

  $ab{e}^{-t}$
• D

  $a{b}^2(1-t)$

Hence, the correct answer is option: 'B'.