Drake is driving a bike on a straight road to his college at a speed of $v$. He realizes that he might be late for his exam.

To rush, he accelerates his bike at a constant acceleration of $a$ for a distance of $L_1$. Then, for the remaining distance $L_2$, he slows down at a constant retardation of $a$ to just reach his college.

Given that $L_2 = k L_1,$ what is the maximum velocity attained during his travel?

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