A car is to be hoisted by elevator to the fourth floor of a parking garage, which is at a height h above the ground. If the elevator can accelerate at a₁, decelerate at a₂, and reach a maximum speed v, determine the shortest time to make the lift, starting from rest and ending at rest. Given:

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h = 48 ft al = 0.6 ft 2 S a2 = 0.3 ft 2 S v = 8- - S