A conveyor can accelerate at a constant 0.3 ft/s², decelerate at a constant 0.7 ft/s², and move at a maximum speed of 6 ft/s. What is the fastest time it would take to move a package a distance of 27...

Extracted text: A conveyor can accelerate at a constant 0.3 ft/s², decelerate at a constant 0.7 ft/s², and move at a maximum speed of 6 ft/s. What is the fastest time it would take to move a package a distance of 27 ft? The package must begin and end at rest. Sketch the acceleration, velocity, and position as a function of time to communicate (and think through) your answer.