Designing an Elevator for a Hospital: Maximum Speed and Newton's Laws Explained

[physstudent1]

"You are designing an elevator for a hospital. The force exerted on a passenger by the floor of the elevator is not to exceed 1.6 times the passenger's weight. The elevator accelerates upward with constant acceleration for a distance of 3m and then slows down. What is the maximum speed of the elevator?"

The answer in the back of the book is 5.9 m/s.

When I drew a FBD and solved for acceleration I came up with 5.9 though. I made my equation 1.6mg - mg = ma. Then I canceled m out of everything and got a to be 5.9 m/s^2 what did I do wrong? Obviously this cannot be the acceleration if the max speed is this.

 

[physics.guru]

Excellent work so far, but you need to finish the problem. You have calculated the net acceleration acting on the elevator. From the problem, we see the elevator undergoes constant acceleration through a displacement of 3m. Kinematically, is there an equation that we can use that gives the final velocity in terms of the initial velocity (zero), acceleration, and displacement?

 

[physstudent1]

yeah.

Oh I see thanks a lot:)