Graph of Elevator's Velocity: Understanding Displacement and Distance Traveled

[reminiscent]

Homework Statement

Homework Equations

The Attempt at a Solution

This is more of a help with understanding problem. I understand a) and b), but for c), I don't understand:
1. Why is the distance from t=12-16 -20 m and not +20 m? Isn't there a positive slope? I thought this question was asking for distance traveled, not displacement?
2. My attempt at c) was to use the equation y(t)-y0 = 1/2(v0+v(t))t, but my answer was 325 m. y0=+75 m, v0=20 m/s, v(t)=5 m/s, and t=20s. What did I do wrong?

 

[TSny]

Part (c) asks for distance traveled, but part (d) asks for the final position.

 

[reminiscent]

Part (c) asks for distance traveled, but part (d) asks for the final position.

So what did I do wrong in the equation I set up in d)?

 

[TSny]

y(t)-y0 = 1/2(v0+v(t))t

The average velocity is not 1/2(v0+v(t)) for part (d) because the acceleration is not constant over the entire time interval.

 

[reminiscent]

The average velocity is not 1/2(v0+v(t)) for part (d) because the acceleration is not constant over the entire time interval.

Oh okay, I understand now. Thanks. But what about the distance from t=12-16 seconds? Why is it -20 m and not +20 m?