Master Manipulation (Kinematics)

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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