The acceleration experienced by a moving boat after is engine is cut-off, is given by $a=-k{v}^3,$ where $k$ is a constant. If $v_0$ is the magnitude of velocity at cut-off, then the magnitude of the velocity at time $t$ after the cut off is

• A

  $\frac{v_0}{2kt{v}_0^2}$
• B

  $\frac{v_0}{1+2 kt{v}_0^2}$
• C

  $\frac{v_0}{\sqrt{1-2 k v_0^2}}$
• Correct answer
  D

  $\frac{v_0}{\sqrt{1+2 kt{v}_0^2}}$

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