Master Manipulation (Kinematics)

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

To rush, he accelerates his bike at a constant acceleration of aa for a distance of L1L_1. Then, for the remaining distance L2L_2, he slows down at a constant retardation of aa to just reach his college.

Given that L2=kL1,L_2 = k L_1, what is the maximum velocity attained during his travel?

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