A car in one dimensional motion with initial speed $v_0$ is accelerated with constant acceleration $a_0$ for a distance $s$. Each time the car travels a distance $s=v_0^2 / 2 a_0$, the acceleration of the car is reduced by a multiplying factor $\lambda \lt 1$. If the final speed of the car doubles (at a very large distance from the starting point) then the value of $\lambda$ is

• A

  $4 / 5$
• B

  $1 / \sqrt{3}$
• C

  $3 / 4$
• Correct answer
  D

  $2 / 3$

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