$A$ man is at a distance $d$ behind a bus. The bus starts from rest and moves away from the man with a constant acceleration $a$. At the same time,the man starts running towards the bus with a constant velocity $v$. Which of the following statements are correct?

• A
  The man catches the bus if $v \geq \sqrt{2ad}$.
• B
  If the man just catches the bus,the time taken will be $t = \frac{v}{a}$.
• C
  Both $(a)$ and $(b)$ are correct.
• D
  The man will catch the bus if $v \geq \sqrt{ad}$.