$\mathrm{A}$ and $\mathrm{B}$ participate in a race with acceleration $a_1$ and $a_2$, respectively. $\mathrm{A}$ reaches $t$ times earlier than $\mathrm{B}$ at finish line and their velocities at finish line are $v_1$ and $v_2$, respectively. If difference between their velocities is $v$, then find the value of $v$

• A

  $\frac{a_1+a_2}{2}t$
• Correct answer
  B

  $\sqrt{a_1{a}_2}t$
• C

  $\frac{a_1{a}_2}{a_1+a_2}t$
• D

  $\frac{2a_1{a}_2}{a_1+a_2}t$

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