An elevator starts from rest. It’s acceleration is plotted against time. When it comes to rest it’s height above the starting point is

Question

Now velocity can be found by calculating the area under the slope. But that turns out to be 0, which is weird. It’s probably because I haven’t understood reading the graphs yet. It’s a simple question, but I still need help solving it.

$$Area=8-8=0$$ Which is obviously wrong. How should I do this?

Answer 1

The elevator accelerates from rest at $2$ m/s$^2$ for $4$ seconds so it will reach a velocity of $2\cdot4 = 8$ m/s. It then continues at $8$ m/s for $4$ seconds, then decelerates at $-2$ m/s$^2$ for $4$ seconds back to zero velocity.

To get the distance traveled (height), as the acceleration is uniform, it's the average velocity of each segment times the time. This will be $4\cdot 4 + 8\cdot 4 + 4\cdot 4 = 64$ m.

Answer 2

Draw velocity and time graph , area will give you height. it will be v=2t ,v=8 , v=-2t respectively for your intervals it's a trapezoid of height 8 . you can take it from here